a eulerian lagrangian numerical scheme for the dispersion convection equation using conjugate space time grids abstract a new numerical scheme is proposed for the dispersion convection equation which combines the utility of a fixed grid in eulerian coordinates with the computational power of the lagrangian method convection is formally decoupled from dispersion in a manner which does not leave room for ambiguity the resulting convection problem is solved by the method of characteristics on a grid fixed in space dispersion is handled by finite elements on a separate grid which may but need not coincide wit the former at selected points in spacetime information is projected from one grid to another by local interpolation the conjugate grid method is implemented by linear finite elements in conjunction with piecewise linear interpolation functions and applied to five problems ranging from predominant dispersion to pure convection the results are entirely free of oscillations numerical dispersion exists but can be brought under control either by reducing the spatial increment or by increasing the time step size of the grid used to solve the convection problem contrary to many other methods best results are often obtained when the courant number exceeds 1

a probabilistic collocation eulerian lagrangian localized adjoint method on sparse grids for assessing co2 leakage through wells in randomly heterogeneous porous media abstract we develop a probabilistic collocation eulerian lagrangian localized adjoint method on sparse grids for assessing co2 leakage through wells in randomly heterogeneous porous media by utilizing the intrinsic mathematical numerical and physical properties of the mathematical model we model the process in which co2 is injected into a deep aquifer spreads within the aquifer and upon reaching a leaky well rises up to a shallower aquifer to quantify the leakage rate which depends on the pressure build up in the aquifer due to injection and the buoyancy of co2 the underlying eulerian lagrangian framework has high potential to improve the efficiency and accuracy for the numerical simulation of complex flow and transport processes in co2 sequestration the sparse grid probabilistic collocation framework adds computationally efficient uncertainty quantification functionality onto pre existing eulerian lagrangian methods in a nonintrusive manner it also provides a scalable framework to consider uncertainty in a straightforward parallel manner preliminary numerical experiments show the feasibility and potential of the method

asymptotic properties of moment estimators for overdispersed counts and proportions summary consistency and asymptotic normality of moment estimates of regression parameters and an overdispersion parameter are shown for data with extra binomial and extrapoisson variation the asymptotic covariance of the regression parameters is found to be unaffected by estimation of the overdispersion parameter the moment estimates may be obtained using iterated weighted least squares

an optimal order error estimate for the mass conservative characteristic finite element scheme abstract the mass conservative characteristic mcc finite element scheme preserves the mass balance which is an important property in the numerical simulation of the convection diffusion problems in this paper an optimal order error estimate is obtained for the model problem in one space dimension the convergence rate is o h 2 t in the l l 2 norm for the linear finite element some numerical examples are given to confirm the conclusion

robust estimation of the variance in moment methods for extra binomial and extra poisson variation when faced with data in the form of overdispersed counts or proportions moment methods allow consistent parameter estimation when only the form of the mean and variance is specified if the variance form is misspecified these methods still yield consistent parameter estimates though with lower efficiency and the variances of the estimates will be inconsistent a variance correction is available that yields consistent variance estimates in these circumstances the asymptotic and small sample efficiencies of this correction are calculated and its performance under variance misspecification is studied a group randomized breast self examination prevention study that is now underway serves as a focal point for the study of these properties the use of the variance correction in modelling is illustrated on a teratology data set

the role of the pressure in the partial regularity theory for weak solutions of the navier stokes equations we study the role of the pressure in the partial regularity theory for weak solutions of the navier stokes equations by introducing the notion of dissipative solutions due to duchon robert we will provide a generalization of the caffarelli kohn and nirenberg theory our approach gives a new enlightenment of the role of the pressure in this theory in connection to serrin s local regularity criterion

the conservative characteristic fd methods for atmospheric aerosol transport problems in the paper we develop the new conservative characteristic finite difference methods c cfd for the atmospheric aerosol transport problems we propose the time second order and spatial high order conservative characteristic finite difference methods for the aerosol vertical advection diffusion process and the two dimensional conservative characteristic finite difference methods for aerosol horizontal transport process in the second order splitting algorithm based on the characteristic form of advection diffusion equations tracking back along the characteristic curve we treat the integrals over the tracking cells at the previous time level by the conservative interpolations and propose to treat the diffusion terms by the average along the characteristics where the high order discrete fluxes are obtained by approximating the cumulative mass function and are continuous at the tracking points the important feature is that the proposed c cfd schemes preserve mass and have second order accuracy in time and high order accuracy in space numerical tests are taken to show the accuracy in time and space and mass conservation of our c cfd schemes compared with the standard cfd method a real case of air quality modelling during the 2008 beijing olympics and a severe haze in north china are further simulated and analyzed by using our c cfd algorithm simulated results are in good agreement with observations the developed c cfd algorithm can be used for efficiently solving large scale atmospheric aerosol transport problems

characteristic stabilized finite element method for the transient navier stokes equations abstract based on the lowest equal order conforming finite element subspace xh mh i e p1 p1 or q1 q1 elements a characteristic stabilized finite element method for transient navier stokes problem is proposed the proposed method has a number of attractive computational properties parameter free avoiding higher order derivatives or edge based data structures and averting the difficulties caused by trilinear terms existence uniqueness and error estimates of the approximate solution are proved by applying the technique of characteristic finite element method finally a serious of numerical experiments are given to show that this method is highly efficient for transient navier stokes problem

a note on in situ estimates of sorption using push pull tests 1 a sensitivity analysis reveals that large uncertainty exists in estimates of solute retardation factor r made from sorption push pull tests a simplified push pull data interpretation method for estimating instantaneous linear sorption in confined aquifers is developed the new method is less restrictive in its application than the conventional method that uses an approximate analytical solution to the push pull test problem

time stepping along characteristics with incomplete iteration for a galerkin approximation of miscible displacement in porous media miscible displacement of one incompressible fluid by another in a porous medium is modeled by a nonlinear coupled system of two partial differential equations the pressure equation is elliptic while the concentration equation is parabolic but normally convection dominated a sequential backward difference time stepping scheme is defined it approximates the pressure by a standard galerkin procedure and the concentration by a combination of a galerkin method and the method of characteristics optimal convergence rates in l 2 and h 1 are demonstrated for this scheme and for a modified version in which the algebraic equations at each time step are solved approximately by a limited number of preconditioned conjugate gradient iterations time stepping along the characteristics of the hyperbolic part of the concentration equation is shown to result in smaller time truncation errors than those of standard methods numerical results published elsewhere have confirmed that larger time steps are appropriate

some exact solutions of convection diffusion and diffusion equations we examine solutions of the convection diffusion equation during steady radial flow in two and three dimensions with diffusivity proportional to pn with p the peclet number in two dimensions closed form solutions of the laplace transformed equation occur only for n 1 and n 2 and in three dimensions only for n 5 4 and n 2 the inversions for n 1 two dimensions and 5 4 three dimensions cannot be expressed in closed form on the other hand the value n 2 proposed by de gennes 1983 leads to simple exact solutions both in two dimensions and in three in both cases a change of variable gives a one dimensional equation with constant coefficients exact instantaneous and continuous point source solutions for radial flow in two and three dimensions are thus established in general finite difference methods are needed for arbitrary n relevant instantaneous and continuous point source diffusion solutions are developed for radial two and three dimensional systems these represent small time solutions useful for initiating the finite difference solutions for convection diffusion with arbitrary n

an operator splitting method for nonlinear convection diffusion equations we present a semi discrete method for constructing approximate solutions to the initial value problem for the m dimensional convection diffusion equation u t nabla cdot vec f u varepsilon delta u the method is based on the use of operator splitting to isolate the convection part and the diffusion part of the equation in the case m 1 dimensional splitting is used to reduce the m dimensional convection problem to a series of one dimensional problems we show that the method produces a compact sequence of approximate solutions which converges to the exact solution finally a fully discrete method is analyzed and demonstrated in the case of one and two space dimensions

an investigation of eulerian lagrangian methods for solving heterogeneous advection dominated transport problems numerical simulation of solute transport in heterogeneous porous media is greatly complicated by the large velocity and concentration gradients induced by spatial variations in hydraulic conductivity eulerian lagrangian methods for solving the transport equation can give accurate solutions to heterogeneous problems if their interpolation algorithms are properly selected this paper compares the performance of four eulerian lagrangian solvers that rely on linear quadratic cubic spline and taut spline interpolators in each case a tensor product decomposition is used to reduce the general n dimensional interpolation problem to a sequence of n one dimensional problems comparisons of a set of test problems indicate that the linear and taut spline interpolators are dispersive while the quadratic and cubic spline interpolators are oscillatory the cubic and taut spline interpolators give consistently better accuracy than the more conventional linear and quadratic alternatives simulation experiments in two and three dimensional heterogeneous media indicate that the taut spline interpolator which is applied here for the first time to a solute transport problem is able to yield accurate essentially nonoscillatory solutions for high grid peclet numbers the cubic spline interpolator requires significantly less computational effort to achieve performance comparable to the other methods

a new formula for the analytical solution of the radial dispersion problem a new formula is presented for the analytical solution of the radial dispersion problem which analyzes the dispersive transport of a tracer in radial flow from a recharge well this formula is simpler than a solution presented by previous investigators but the two solutions are shown to be equivalent because the analytical solution consists of an integral of an oscillatory function it is evaluated as an alternating series the terms of which are the integrals over successive half cycles of the integrand an efficient algorithm is used to accelerate convergence of the series the accuracies of previous solutions obtained by finite difference numerical laplace transform and perturbation methods are examined by comparison with the analytical solution numerical values of the solution are tabulated for readers interested in checking the accuracies of solute transport codes

toward an oscillation free mass conservative eulerian lagrangian transport model ten numerical schemes to reduce spurious oscillations in transport simulations were implemented and tested in a eulerian lagrangian control volume finite element model the schemes included both new and existing flux corrected transport fct algorithms and nonlinear filters the ability of the methods to eliminate numerical oscillations while preserving mass and minimizing the introduction of numerical diffusion was compared in 2d tests of varying complexity the application of local mass correction algorithms was shown to be vital to avoid the introduction of mass errors by fct while none of the methods emerged as optimal for all cases a new fct method with a local mass correction scheme and a nonlinear filter can be recommended as the best approaches in general the method of choice depends on the problem being solved in particular on the concentration gradients and on the grid resolution

an evaluation of boundary conditions for one dimensional solute transport 1 mathematical development the laplace transform method is employed to obtain the solution to several boundary value problems in which mixing occurs in reservoirs attached to a porous medium flow is assumed to be uniformly one dimensional throughout the porous medium solutions are obtained for both continuous and discontinuous concentrations at the reservoir medium boundary and for resident and flux averaged concentrations a mass balance conducted on each solution shows that neither continuity condition can be proved generally superior an evaluation of the parametric sensitivity of the solutions is also conducted and shows that the distinction between the continuity conditions and the flux and resident concentrations is only important at small peclet numbers the only exception to this is the distinction between flux averaged versus resident continuous concentrations in a finite solution domain in this case the flux concentrations were found to be insensitive to the volume of the downstream reservoir and consequently the flux and resident concentrations can differ substantially for larger reservoirs in consideration of the general behavior of the solutions three conceptual problems were identified which must be investigated by physical modeling 1 determination of the appropriate solution at small peclet number 2 the possibility that dispersive mass flux occurs from the upstream reservoir under conditions of continuous concentration and 3 the use of the flux transformation for continuous concentration in a finite solution domain the physical modeling is discussed in a companion paper

a finite volume eulerian lagrangian localized adjoint method for solution of the contaminant transport equations in two dimensional multiphase flow systems an eulerian lagrangian localized adjoint method ellam numerical solution is developed for the multiphase contaminant transport equations in two dimensions the ellam uses finite volume test functions in the space time domain defined by the characteristics of the hyperbolic part of the governing equation the use of the characteristics results in an approximation that allows large time steps while still maintaining accurate solutions this greatly reduces the computational effort required to find solutions to the advection dispersion equation combination of the finite volume test functions with the conservative form of the governing equation results in a local conservation of mass property for problems with a constant saturation such as that of contaminant transport in the saturated zone this property is highly advantageous as the resulting numerical approximation conserves mass both globally and locally for problems with a variable saturation the requirement of local conservation of mass is too stringent particularly around first type boundaries where oscillations can occur because of errors inherent in the numerical determination of fluid velocities and in the backtracking routine a combined conservative nonconservative ellam is developed with an ellam formulation based on the nonconservative form of the governing equation being applied to subdomains intersecting first type boundaries and a conservative ellam being used for all other subdomains the combined conservative nonconservative ellam is compared to a galerkin finite element scheme and is found to have greatly superior performance requiring far fewer time steps to obtain a solution of equivalent accuracy

an ellam scheme for advection diffusion equations in two dimensions we develop an eulerian lagrangian localized adjoint method ellam to solve two dimensional advection diffusion equations with all combinations of inflow and outflow dirichlet neumann and flux boundary conditions the ellam formalism provides a systematic framework for implementation of general boundary conditions leading to mass conservative numerical schemes the computational advantages of the ellam approximation have been demonstrated for a number of one dimensional transport systems practical implementations of ellam schemes in multiple spatial dimensions that require careful algorithm development are discussed in detail in this paper extensive numerical results are presented to compare the ellam scheme with many widely used numerical methods and to demonstrate the strength of the ellam scheme

on the transport diffusion algorithm and its applications to the navier stokes equations this paper deals with an algorithm for the solution of diffusion and or convection equations where we mixed the method of characteristics and the finite element method globally it looks like one does one step of transport plus one step of diffusion or projection but the mathematics show that it is also an implicit time discretization of thepde in lagrangian form we give an error bound h t h h t in the interesting case that holds also for the navier stokes equations even when the reynolds number is infinite euler equation

a hybrid mixed finite element method for miscible displacement problem with mcc procedure abstract a new combined method is developed for solving incompressible miscible displacement in porous media in this method a hybrid mixed element method is constructed for the pressure and velocity equation while a mass conservative characteristic mcc finite element method is presented for concentration equation the introduction of these two numerical algorithms not only makes the coefficient matrixes symmetric positive definite but also keeps the mass balance the stability and consistence of this method are analyzed and the optimal error estimates in l2 norm for velocity concentration and pressure are derived finally some numerical results are presented

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

an explicit unconditionally stable numerical solution of the advection problem in irrotational flow fields 1 a new methodology for the eulerian numerical solution of the advection problem is proposed the methodology is based on the conservation of both the zero and the first order spatial moments inside each element of the computational domain and leads to the solution of several small systems of ordinary differential equations since the systems are solved sequentially one element after the other the method can be classified as explicit the proposed methodology has the following properties 1 it guarantees local and global mass conservation 2 it is unconditionally stable and 3 it applies second order approximation of the concentration and its fluxes inside each element limitation of the procedure to irrotational flow fields for the 2 d and 3 d cases is discussed the results of three 1 d and 2 d literature tests are compared with those obtained using other techniques a new 2 d test with radially symmetric flow is also carried out

partial regularity for the navier stokes equations with a force in a morrey space abstract in the paper we address the partial regularity of solutions of the navier stokes system earlier we have proved that the one dimensional parabolic hausdorff measure of the singular set is zero under the assumption that the force f belongs locally to l 5 3 here we prove the same statement under a more general assumption that the morrey norm in l 5 7 10 7 of the force is sufficiently small we do so by establishing a fractional integration theorem using the morrey spaces and by a suitable iteration using a localized version of the morrey norm

a galerkin characteristic unified finite element method for moving thermal fronts in porous media abstract we investigate the performance of a unified finite element method for the numerical solution of moving fronts in porous media under non isothermal flow conditions the governing equations consist of coupling the darcy equation for the pressure to two convection diffusion reaction equations for the temperature and depth of conversion the aim is to develop a non oscillatory unified galerkin characteristic method for efficient simulation of moving fronts in porous media the method is based on combining the modified method of characteristics with a galerkin finite element discretization of the governing equations the main feature of the proposed unified finite element method is that the same finite element space is used for all solutions to the problem including the pressure velocity temperature and concentration analysis of convergence and stability is also presented in this study and error estimates in the l 2 norm are established for the numerical solutions in addition due to the lagrangian treatment of convection terms the standard courant friedrichs lewy condition is relaxed and the time truncation errors are reduced in the diffusion reaction part we verify the method for the benchmark problem of moving fronts around an array of cylinders the numerical results obtained demonstrate the ability of the proposed method to capture the main flow features

on the regularity of weak solutions to the magnetohydrodynamic equations abstract in this paper we study the regularity of weak solution to the incompressible magnetohydrodynamic equations we obtain some sufficient conditions for regularity of weak solutions to the magnetohydrodynamic equations which is similar to that of incompressible navier stokes equations moreover our results demonstrate that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solution to the magneto hydrodynamic equations

adaptive eulerian lagrangian finite element method for advection dispersion a new adaptive finite element method is proposed for the advection dispersion equation using an eulerian lagrangian formulation the method is based on a decomposition of the concentration field into two parts one advective and one dispersive in a rigorous manner that does not leave room for ambiguity the advective component of steep concentration fronts is tracked forward with the aid of moving particles clustered around each front away from such fronts the advection problem is handled by an efficient modified method of characteristics called single step reverse particle tracking when a front dissipates with time its forward tracking stops automatically and the corresponding cloud of particles is eliminated the dispersion problem is solved by an unconventional lagrangian finite element formulation on a fixed grid which involves only symmetric and diagonal matrices preliminary tests against analytical solutions of one and two dimensional dispersion in a uniform steady state velocity field suggest that the proposed adaptive method can handle the entire range of peclet numbers from 0 to with courant numbers well in excess of 1

mass balance errors when solving the convective form of the transport equation in transient flow problems 1 the original divergence form of the solute transport equation expresses the mass balance of solutes in groundwater the alternative convective form can be obtained by subtracting the flow equation multiplied by concentration from the original form many investigators prefer the latter because it facilitates the use of lagrangian or mixed eulerian lagrangian numerical methods for solution however it performs very poorly in transient contaminant transport problems with large temporal variations in water content we propose an alternative to overcome this difficulty it consists of evaluating the water content at time level k 1 if concentration in the convective term is evaluated at time level k for this reason we have called it reverse time weighting whereas we call an evaluation of the water content at time level k straight time weighting we show that reverse time weighting improves significantly over straight time weighting not only in terms of mass balance errors but also in terms of concentration errors

a fully mass and volume conserving implementation of a characteristic method for transport problems the characteristics mixed method considers the transport not of a single point or fluid particle but rather the mass in an entire region of fluid this mass is transported along the characteristic curves of the hyperbolic part of the transport equation and the scheme thereby produces very little numerical dispersion conserves mass locally and can use long time steps however since the shape of a characteristic trace back region must be approximated in numerical implementation its volume may be incorrect resulting in inaccurate concentration densities and further inaccurate reaction dynamics we present a simple modification to the characteristics mixed method that conserves both mass and volume of the transported fluid regions our algorithm also handles boundary conditions through a space time change of variables in the trace back routines which allows the boundary to be treated as if it were interior to the domain nearly point sources such as wells present special difficulties since characteristic trace back curves converge in their vicinity we also present techniques that allow one to conservatively implement wells the techniques are illustrated in five numerical examples

numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form cu t bu x au x x f optimal order error estimates in l 2 and w 1 2 are derived for the finite element procedure various error estimates are presented for a variety of finite difference methods the estimates show that for convection dominated problems b gg a these schemes have much smaller time truncation errors than those of standard methods extensions to n space variables and time dependent or nonlinear coefficients are indicated along with applications of the concepts to certain problems described by systems of differential equations

error estimates for discontinuous galerkin approximations of implicit parabolic equations we analyze the classical discontinuous galerkin method for implicit parabolic equations symmetric error estimates for schemes of arbitrary order are presented the ideas developed allow certain assumptions frequently required in previous work to be relaxed for example different discrete spaces are allowed at each time step and the spatial operator is not required to be self adjoint or independent of time error estimates are posed in terms of projections of the exact solution onto the discrete spaces and are valid under the minimal regularity guaranteed by the natural energy estimate these projections are local and enjoy optimal approximation properties when the solution is sufficiently regular

a method for implementing dirichlet and third type boundary conditions in ptrw simulations we present an efficient and accurate numerical method for implementing dirichlet boundary conditions in particle tracking random walk ptrw simulations of advective dispersive transport this is a challenge because defining concentrations for dirichlet boundary conditions requires invoking control volumes of some kind which are not natural to the lagrangian based ptrw concept our method performs a galerkin projection of ptrw based particle densities onto control volumes that discretize the boundary thus we obtain concentration values at the boundary condition and can control the particle release rates such that the prescribed boundary values are met this allows for complex shaped internal and external boundaries where concentration values are fixed to prescribed values third type boundary conditions can be addressed as well we test and illustrate the properties and behavior of our method in a series of test cases the results are benchmarked against the conceptually related semianalytical method masst multiple analytical source superposition technique and to those of a finite element method fem while masst is restricted to uniform velocity fields due to the underlying analytical solutions fem is limited in heterogeneous velocity fields at large peclet numbers by numerical dispersion in the feasible discretization range the results demonstrate that our proposed method performs better than the other methods in both regimes

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100

partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations in this paper we study the local behavior of the solutions to the three dimensional magnetohydrodynamic equations we are interested in both the uniform gradient estimates for smooth solutions and regularity of weak solutions it is shown that in some neighborhood of x0 t0 the gradients of the velocity field u and the magnetic field b are locally uniformly bounded in l norm as long as that either the scaled local l2 norm of the gradient or the scaled local total energy of the velocity field is small and the scaled local total energy of the magnetic field is uniformly bounded these estimates indicate that the velocity field plays a more dominant role than that of the magnetic field in the regularity theory as an immediately corollary we can derive an estimates of hausdorff dimension on the possible singular set of a suitable weak solution as in the case of pure fluid various partial regularity results are obtained as consequences of our blow up estimates

a semi lagrangian method for the weather options of mean reverting brownian motion with jump diffusion abstract the weather options were created to enable companies to hedge against climate risks however the valuation of weather options is complex since the underlying temperature process has no negotiable price this paper presents a new weather option pricing model which is governed by a stochastic underlying temperature following a mean reverting browning motion with jump diffusion under the assumption of mean self financing consequently a two dimensional partial integro differential equation pide is derived to value the weather based options the numerical techniques applied in this paper are based on a semi lagrangian method slm in which at each time step a set of one dimensional partial integro differential equations are solved and the solution of each pide is updated using semi lagrangian time stepping in addition monotonicity stability and the convergence results of the discrete schemes are also derived in this paper lastly this paper values a series of european hdd based weather put options using slm and highlights the key details of the numerical implementation

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

a mass conservative characteristic fe scheme for optimal control problems governed by convection diffusion equations abstract in this paper we develop a mass conservative characteristic finite element scheme for optimal control problems governed by linear singularly perturbed convection diffusion equations we discuss the case that the velocity fields are non divergence free the space discretization of the state variable is done by piecewise linear continuous functions whereas the control variable is approximated by piecewise constant functions due to the limitation of the regularity the scheme preserves the mass balance for the original state equation we derive a priori error estimates for both the control and state approximations some numerical examples are presented to show the efficiency of the proposed scheme

a two grid method for incompressible miscible displacement problems by mixed finite element and eulerian lagrangian localized adjoint methods abstract in this paper we present a scheme for solving two dimensional miscible displacement problems using eulerian lagrangian localized adjoint methods and mixed finite element methods since only the velocity and not the pressure appears explicitly in the concentration equation an eulerian lagrangian localized adjoint method is used to solve the concentration equation and a mixed finite element method is used for the pressure equation to linearize and decouple the mixed method equations we use a two grid algorithm based on the newton iteration method for this fully discrete problems first we solve the original nonlinear equations on the coarse grid then we solve the linearized problem on the fine grid using newton iteration once it is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy h o h 1 2 in this paper

a two grid eulerian lagrangian localized adjoint method to miscible displacement problems with dispersion term abstract in this paper we propose a novel two grid method of eulerian lagrangian localized adjoint method ellam mixed finite element method mfem solutions for nonlinear and coupled miscible displacement problems which describe complex fluid flow processes in porous media an ellam is used to solve the nonlinear convection diffusion equation for concentration and we present a mfem to compute the pressure equation for the pressure and darcy velocity a two grid scheme is investigated to linearize and decouple the mixed method equations it is illustrated that the coarse space can be selected as coarse as h o h 1 2 and the asymptotically optimal approximation as the nonlinear schemes can be still achieved as a result a large class of such nonlinear and coupled problems can be solved efficiently with large time steps

significance testing for correlated binary outcome data multiple logistic regression is a commonly used multivariate technique for analyzing data with a binary outcome one assumption needed for this method of analysis is the independence of outcome for all sample points in a data set in ophthalmologic data and other types of correlated binary data this assumption is often grossly violated and the validity of the technique becomes an issue a technique has been developed rosner 1984 that utilizes a polychotomous logistic regression model to allow one to look at multiple exposure variables in the context of a correlated binary data structure this model is an extension of the beta binomial model which has been widely used to model correlated binary data when no covariates are present in this paper a relationship is developed between the two techniques whereby it is shown that use of ordinary logistic regression in the presence of correlated binary data can result in true significance levels that are considerably larger than nominal levels in frequently encountered situations this relationship is explored in detail in the case of a single dichotomous exposure variable in this case the appropriate test statistic can be expressed as an adjusted chi square statistic based on the 2 x 2 contingency table relating exposure to outcome the test statistic is easily computed as a function of the ordinary chi square statistic and the correlation between eyes or more generally between cluster members for outcome and exposure respectively this generalizes some previous results obtained by koval and donner 1987 in festschrift for v m joshi i b macneill ed vol v 199 224 abstract truncated at 250 words

multiblock hybrid grid finite volume method to solve flow in irregular geometries in this work a finite volume based finite element method is suitably developed for solving incompressible flow and heat transfer on collocated hybrid grid topologies the method is generally applicable to arbitrarily shaped elements and orientations and thus challenges the potential to unify many of the different grid topologies into a single formulation the key point in this formulation is the correct estimation of the convective and diffusive fluxes at the cell faces using a novel physical influence scheme this scheme remarkably enhances the achieved solution accuracy it is shown that the extended formulation is robust enough to treat any combination of multiblock meshes with dual element shape employments in this regard the solution domain is broken up into a number of different multiblock arrangements in which each block is filled with only one type of finite element shape the combined grid can decrease the computational time and memory requirements and increase the numerical accuracy the results of the extended formulation are validated against different benchmark and other solutions the current results are in excellent agreement with the other solutions without exhibiting any disturbances around the block boundaries

conservative multimoment transport along characteristics for discontinuous galerkin methods a set of algorithms based on characteristic discontinuous galerkin methods is presented for tracer transport on the sphere the algorithms are designed to reduce message passing interface communica

a numerical inversion of the laplace transform solution to radial dispersion in a porous medium a special form of the numerical inversion of the laplace transform described by stehfest 1970 is applied to the transformed solution of dispersion in a radial flow system in a porous medium the inversion is extremely simple to use because the weighting coefficients depend only on the number of terms used in the computation and not upon the transform solution as required by most numerical inversion techniques the result obtained by use of this approximate inversion of the radial dispersion problem reproduced the curves obtained previously by hoopes and harleman 1967 with a finite difference scheme

a cbs type stabilizing algorithm for the consolidation of saturated porous media the presented method stems from the works by zienkiewicz and co workers for coupled fluid thermal problems starting from the early 1990s they propose algorithms to overcome the difficulties connected to the application of the fem to the area of fluid mechanics which include the problems of singular behaviour in incompressibility and the problems connected to convective terms the major step forward was to introduce the concept of characteristic lines the particle paths in a simple convection situation for a class of problems with a single scalar variable the equations in the characteristic co ordinates regain self adjointness the procedure is called characteristic based split algorithm cbs we use here a cbs type procedure for a saturated deformable elastic porous medium in which the fluid velocity is governed by darcy s equation which comes directly from navier stokes ones the physical mathematical model is a fully coupled one and is here used to study an incompressible flow inside a continuum with incompressible solid grains the power of the adopted algorithm is to treat the basic equations in their strong form and to transform a usual u p problem into a u v p one where u generally indicates the displacement of the solid matrix and p and v the pressure and velocity of the fluid respectively attention is focused on the expression of darcy s velocity which is considered as the starting point of the algorithm the accuracy of the scheme is checked by comparing the present predictions in a typical consolidation test with available analytical and numerical u p solutions a good fitting among different results has been obtained it is further shown that the procedure eliminates the oscillations at the onset of consolidation typical for many schemes the fem code ed multifield has been used for implementing and testing the procedure copyright 2005 john wiley sons ltd

on the partial regularity theory for the mhd equations abstract we generalize here the celebrated partial regularity theory of caffarelli kohn and nirenberg to the mhd equations in the framework of parabolic morrey spaces this type of parabolic generalization using morrey spaces appears to be crucial when studying the role of the pressure in the regularity theory for the classical navier stokes equations as well as for the mhd equations

solving the advection diffusion equation with the eulerian lagrangian localized adjoint method on unstructured meshes and non uniform time stepping eulerian lagrangian localized adjoint method ellam is used to solve the advection diffusion equation ade which is a very common mathematical model in physics in this work ellam is extended to triangular meshes standard integration schemes which perform well for rectangular grids are improved to reduce oscillations with unstructured triangulations numerical experiments for grid peclet numbers ranking from 1 to 100 show the efficiency of the developed scheme a new algorithm is also developed in order to avoid excessive numerical diffusion when using many time steps with the ellam the basic idea of this approach is to keep the same characteristics for all time steps and to interpolate only the concentration variations due to the dispersion process at the end of each time step although ellam requires a lot of integration points for unstructured meshes it remains a competitive method when using a single or many time steps compared to explicit discontinuous galerkin finite element method

solute transport in divergent radial flow with multistep pumping 1 an efficient approach is developed to analytically evaluate solute transport in a horizontal divergent radial flow field with a multistep injection flow rate and an arbitrary input concentration history by assuming a piecewise steady state flow and transforming the time domain to the cumulative injected flow domain the concentration distribution is found to be completely determined by the total volume of injected flow and independent of specific flow rates thus on the cumulative flow domain the transport problem with a temporally varying velocity field can be transformed into a steady state flow problem linear convolution can then be applied on the cumulative injected flow domain to evaluate the solution for an arbitrarily time dependent input concentration solutions on the regular time domain can be conveniently obtained by mapping the solution on the cumulative injected flow domain to the time domain furthermore we theoretically examine the conditions for the assumption of piecewise steady state flow to be valid on the basis of the critical time scale of the pseudosteady state condition defined as when velocity changes accomplish 99 of their steady state differences and the relative error in the mean travel time of plume front we obtain conditions for neglecting the transitional period between two pumping steps such conditions include the following 1 the duration of a pumping step tp must be longer than the critical time scale tc i e tp tc 25r2s t where r is the radial distance s is the storage coefficient and t is the transmissivity or similarly a maximum problem domain needs to be defined for a given pumping strategy 2 the maximum well pumping rate qmax should satisfy qmax t 25s where is the effective porosity when both conditions are satisfied transitional periods may be neglected

the modified method of characteristics with adjusted advection the mmoc procedure for approximating the solutions of transport dominated diffusion problems does not automatically preserve integral conservation laws leading to mass balance errors in many kinds of flow problems the variant called the mmocaa discussed herein preserves the conservation law at a minor additional computational cost it is shown that its solution in either galerkin or finite difference form converges at the same rates as were proved earlier by dougl as and russell for the standard mmoc procedure

a finite volume eulerian lagrangian localized adjoint method for solution of the advection dispersion equation a new mass conservative method for solution of the one dimensional advection dispersion equation is derived and discussed test results demonstrate that the finite volume eulerian lagrangian localized adjoint method fvellam outperforms standard finite difference methods in terms of accuracy and efficiency for solute transport problems that are dominated by advection for dispersion dominated problems the performance of the method is similar to that of standard methods like previous ellam formulations fvellam systematically conserves mass globally with all types of boundary conditions fvellam differs from other ellam approaches in that integrated finite differences instead of finite elements are used to approximate the governing equation this approach in conjunction with a forward tracking scheme greatly facilitates mass conservation the mass storage integral is numerically evaluated at the current time level and quadrature points are then tracked forward in time to the next level forward tracking permits straightforward treatment of inflow boundaries thus avoiding the inherent problem in backtracking as used by most characteristic methods of characteristic lines intersecting inflow boundaries fvellam extends previous ellam results by obtaining mass conservation locally on lagrangian space time elements details of the integration tracking and boundary algorithms are presented test results are given for problems in cartesian and radial coordinates

numerical analysis of convection diffusion reaction problems with higher order characteristics finite elements part ii fully discretized scheme and quadrature formulas in this paper a higher order lagrange galerkin discretization method is analyzed when applied to a variable coefficient convection possibly degenerated diffusion reaction equation with mixed dirichlet robin boundary conditions in a previous paper a bermu dez m r nogueiras and c va zquez siam j numer anal to appear the proposed second order time discretization scheme has been rigorously introduced for exact and approximated characteristics moreover the l infty l 2 stability property and l infty l 2 error estimates of order o delta t 2 have been obtained as a continuation of that work consistency error estimates of order o delta t 2 h k are obtained for the fully discretized lagrange galerkin scheme moreover adequate quadrature formulas are proposed for the practical implementation of the method with particular finite element spaces finally some numerical tests illustrate the theoretical results and the performance of the combination of second order lagrange galerkin schemes with quadrature formulas

preconditioners for nonsymmetric indefinite linear systems abstract in this paper we develop algorithms for solving nonsymmetric indefinite linear systems by considering the augmented linear systems resulting from a weighted linear least squares problem even though the augmented system is more ill conditioned than the original linear system one can construct preconditioned gmres methods for solving these augmented systems capable of obtaining reasonable approximation of the solution in fewer iterations than the classical ilu preconditioned gmres method for solving the original linear system more specifically we present two different preconditioners for these augmented systems examine the spectral properties of these preconditioned augmented systems and report numerical results to illustrate the effectiveness of these preconditioners

estimation of a common odds ratio under binary cluster sampling we present results from a simulation study for the estimation of a common odds ratio in multiple 2 x 2 tables when the data are correlated within clusters we model the correlation of the data by the beta binomial distribution through a simulation study we compare the mantel haenszel estimator with rao and scott s estimator in terms of their biases observed variances relative efficiencies of their variances and 95 per cent coverage proportions we limit the simulation study to the case where there are the same number of subjects in each cluster and the same number of observations in each row of each stratum when rho 0 we recommend use of the mantel haenszel estimator gamma mh with an unadjusted variance and rao and scott s estimator gamma rsp with a pooled design effect in general when rho 0 we recommend the mantel haenszel estimator gamma mh with an adjusted variance and rao and scott s estimator gamma rsp with a pooled design effect

a spectral lagrange galerkin method for convection dominated diffusion problems abstract the spectral lagrange galerkin method is a numerical technique for time dependent convection diffusion problems based on combining a lagrangian formulation of the equations with the spectral method the resulting scheme can be shown to be unconditionally stable for linear advection diffusion equations and optimal convergence rates may be obtained both the spectral accuracy and the efficiency of the scheme are examined theoretically and by various numerical experiments and extensions of the method to give high accuracy in time are presented

an evaluation of methods for the stratified analysis of clustered binary data in community intervention trials a simulation study is conducted in a community intervention setting several methods of stratified analysis of clustered binary data are compared in terms of empirical significance and empirical power levels they are the mantel haenszel test statistic chi 2 mh the adjusted mantel haenszel test statistic of donald donner chi 2 dd rao scott chi 2 rsn and chi 2 rsp and zhang boos chi 2 zbn and chi 2 zbp wald chi 2 w robust wald chi 2 rw score chi 2 s robust score chi 2 rs and the test statistic based on generalized linear mixed model glmm chi 2 glmm when rho not equal 0 chi 2 mh has inflated type i error and it should not be used when observations are correlated the results also warn of the use of chi 2 rsn and chi 2 rw due to their poor performance in terms of empirical significance level chi 2 zbp and chi 2 glmm have better empirical significance levels as compared to other statistics however chi 2 zbp tends to have lower empirical powers than other statistics when the number of clusters n is less than 24 chi 2 rsp provides the highest empirical powers when rho or 0 1 and n or 12 when rho or 0 01 we recommend the use of chi 2 rs and chi 2 glmm since they have better overall performance in terms of empirical significance levels and empirical power levels

adaptive multiresolution semi lagrangian discontinuous galerkin methods for the vlasov equations we develop adaptive numerical schemes for the vlasov equation by combining discontinuous galerkin discretisation multiresolution analysis and semi lagrangian time integration we implement a tree based structure in order to achieve adaptivity both multi wavelets and discontinuous galerkin rely on a local polynomial basis the schemes are tested and validated using vlasov poisson equations for plasma physics and astrophysics

a modified characteristic finite element method for a fully nonlinear formulation of the semigeostrophic flow equations this paper develops a fully discrete modified characteristic finite element method for a coupled system consisting of the fully nonlinear monge ampere equation and a transport equation the system is the eulerian formulation in the dual space for b j hoskins semigeostrophic flow equations which are widely used in meteorology to model frontogenesis to overcome the difficulty caused by the strong nonlinearity we first formulate at the differential level a vanishing moment approximation of the semigeostrophic flow equations a methodology recently proposed by the authors x feng and m neilan j sci comput 38 2009 pp 74 98 which involves approximating the fully nonlinear monge ampere equation by a family of fourth order quasilinear equations we then construct a fully discrete modified characteristic finite element method for the regularized problem it is shown that under certain mesh constraint the proposed numerical method converges with an optimal order rate of convergence in particular the obtained error bounds show explicit dependence on the regularization parameter varepsilon numerical tests are also presented to validate the theoretical results and to gauge the efficiency of the proposed fully discrete modified characteristic finite element method

finite element methods for nonlinear flows in porous media abstract a model problem is presented for fluid flow in porous media which has numerical difficulties common with many other areas of nonlinear mechanics special finite element techniques are described which have proved useful in alleviating many of these difficulties a modified method of characteristics mixed finite element methods for fluid velocities singularity removal and self adaptive local grid refinement techniques are presented both theoretical and computational results are described together with an indication of the present and future uses of finite element methods in large scale reservoir simulation

a conservative characteristic finite volume element method for solution of the advection diffusion equation abstract we develop a modified characteristic finite volume element method for two dimensional advection diffusion problem in a convex spacial domain using quasi uniform triangular discretization and piecewise linear element this scheme conserves mass globally and locally on the lagrangian space time control volume we give the optimal order h1 norm and optimal l2 norm error estimates finally we present some numerical examples

evaluation of an adjusted chi square statistic as applied to observational studies involving clustered binary data a simple adjustment to the pearson chi square test has been proposed for comparing proportions estimated from clustered binary observations however the assumptions needed to assure the validity of this test have not yet been thoroughly addressed these assumptions will hold for experimental comparisons but could be violated for some observational comparisons in this paper we investigate the conditions under which the adjusted chi square statistic is valid and examine its performance when these assumptions are violated we also introduce some alternative test statistics that do not require these assumptions the test statistics considered are then compared through simulation and an example presented based on real data the simulation study shows that the adjusted chi square statistic generally produces empirical type i errors close to nominal under the assumption of a common intracluster correlation coefficient even if the intracluster correlations are different the adjusted chi square statistic performs well when the groups have equal numbers of clusters

on partial regularity results for the navier stokes equations looking at the regularity results of scheffer respectively caffarelli kohn and nirenberg from a new point of view indicates that estimates for the pressure do not play an essential role in partial regularity results for the navier stokes equations

statistical methods in ophthalmology an adjusted chi square approach ophthalmologic studies often compare several groups of subjects for the presence or absence of some ocular finding where each subject may contribute two eyes to the analysis the values from the two eyes being highly correlated rosner 1982 biometrics 38 105 114 and dallal 1988 biometrics 44 253 257 proposed procedures for testing whether the proportion of affected eyes is the same among the different groups while accounting for the intrasubject correlation in this paper we propose an alternative approach based on a simple adjustment of the standard pearson chi square test for the equality of proportions the suggested approach utilizes information on subjects who supply only one eye to the analysis and readily generalizes to studies in which more than two units of analysis are provided by each subject

multivariate methods in ophthalmology with application to other paired data situations methods are presented for performing multiple regression analyses and multiple logistic regression analyses on ophthalmologic data with normally and binomially distributed outcome variables while accounting for the intraclass correlation between eyes these methods are extended to more general nested data structures where a variable number of subunits are available for each primary unit of analysis as in familial data these methods can also be applied to other types of paired data as in matched studies with a variable matching ratio where one has a continuous outcome variable and wishes to control for other confounding variables while maintaining the matching examples are given of these methods with a group of over 400 patients with retinitis pigmentosa in which spherical refractive error and visual acuity are related to genetic type after the effects of age sex and the presence of cataract have been controlled

finite difference methods for two phase incompressible flow in porous media two phase incompressible flow in porous media is governed by a system of nonlinear partial differential equations convection physically dominates diffusion and the object of this paper is to develop a finite difference procedure that reflects this dominance the pressure equation which is elliptic in appearance is discretized by a standard five point difference method the concentration equation is treated by an implicit finite difference method that applies a form of the method of characteristics to the transport terms a convergence analysis is given for the method

a simple method for the analysis of clustered binary data a simple method for comparing independent groups of clustered binary data with group specific covariates is proposed it is based on the concepts of design effect and effective sample size widely used in sample surveys and assumes no specific models for the intracluster correlations it can be implemented using any standard computer program for the analysis of independent binary data after a small amount of preprocessing the method is applied to a variety of problems involving clustered binary data testing homogeneity of proportions estimating dose response models and testing for trend in proportions and performing the mantel haenszel chi squared test for independence in a series of 2 x 2 tables and estimating the common odds ratio and its variance illustrative applications of the method are also presented

hypothesis testing for proportions with overdispersion summary the properties of likelihood ratio tests and simpler t tests are investigated by simulation under an assumed beta binomial model for parameter values typically found in toxicological studies it is found that likelihood ratio methods are at least as powerful as the simpler approaches and in certain situations can be significantly more powerful

a characteristics mixed covolume method for a convection dominated transport problem in this paper we propose a characteristics mixed covolume method for approximating the solution to a convection dominated transport problem the method is a combination of characteristic approximation to handle the convection term in time and mixed covolume method spatial approximation to deal with the diffusion term the velocity and press are approximated by the lowest order raviart thomas mixed finite element space on rectangles the projection of a mixed covolume element is introduced we prove its first order optimal rate of convergence for the approximate velocities in the l 2 norm as well as for the approximate pressures in the l 2 norm

likelihood inference in a correlated probit regression model correlated binary observations arise in a variety of applications for example in animal studies the term litter effect is used to describe the greater alikeness of responses within a litter as compared to that between litters at a given set of experimental conditions in a setting that motivated this work cells on individual atomic bomb survivors were scored as to the presence or absence of chromosomal aberrations the number of aberrant cells varied among subjects at a specified radiation exposure estimate age at exposure city of exposure and sex in a manner that substantially exceeds that consistent with a binomial error structure otake prentice 1984 this extra binomial variation or overdispersion reflects the fact that the binary response of cells from a given survivor tend to be more alike than are the responses of cells from distinct survivors having the same estimated radiation exposure level and other covariate values such overdispersion may result from individual differences in susceptibility to radiation damage from omitted covariates or most plausibly in this setting from substantial random errors in the estimated radiation exposure levels failure to acknowledge overdispersion may lead to serious underestimation of the standard errors associated with regression parameter estimates and to unduly precise inferences

simulation of miscible displacement in porous media by a modified uzawa s algorithm combined with a characteristic method abstract miscible displacement in porous media is modeled by a nonlinear coupled system of two partial differential equations the pressure equation which is elliptic and the concentration equation which is parabolic but usually convection dominated in this paper we focus on some computational difficulties in the simulation of this problem in order to obtain accurate approximation for velocity we implement a modified uzawa s algorithm for the pressure equation with a full permeability tensor including strong heterogeneity and anisotropy for handling the convection dominance over diffusion we employ a modified method of characteristics for the concentration equation numerical simulation results show that the combination of the modified method of characteristics and the modified uzawa s algorithm is a good choice for the problem in particular the modified method of characteristics dramatically reduces numerical diffusion and non physical oscillation in the approximate concentration and the modified uzawa s algorithm leads to positive definite linear systems with velocity unknowns only and exhibits the accuracy of mixed finite element methods

on boundary conditions and point sources in the finite element integration of the transport equation in the finite element integration of the convection dispersion equation over a groundwater domain boundary conditions of the third or cauchy type may or may not be incorporated with the variational statement while the former development formulation a requires the application of green s first identity to both the convective and the dispersive terms the latter formulation b does not although both approaches are equivalent at the theoretical level they behave differently from a computational standpoint the numerical solution proves more accurate and stable if green s lemma is not applied to the convective term since significant errors arising from the representation of the darcy velocity over the elements are avoided point sources or sinks representing injection or pumping wells can be treated as either sources sinks distributed over a small volume or external boundaries with prescribed contaminant flux it is shown that when the well bore is excluded from the flow field formulation a yields the same matrix addition for an injection abstraction well as formulation b does for an abstraction injection well reciprocity of the results the computational behaviors of these alternative modeling procedures are illustrated with a number of significant numerical examples

an efficient characteristic galerkin scheme for the advection equation in 3 d conventional galerkin based finite element algorithms perform poorly when modeling advective transport here we develop and test a characteristic galerkin scheme to solve the unsteady three dimensional advective transport equation the algorithm uses tracking of the gaussian quadrature points to project the information from the eulerian background grid to the lagrangian grid numerical experiments were carried out to investigate the performance of this scheme despite speculations to the contrary in the literature this scheme does not suffer from instability problems further it is conservative and shows good phase characteristics with slight numerical diffusion we conclude that the characteristic galerkin method is a viable and efficient scheme for solving advection problems in three dimensions

eulerian lagrangian localized adjoint methods for a nonlinear advection diffusion equation eulerian lagrangian localized adjoint methods ellam are developed for the non linear buckley leverett equation which is characterized by degenerate diffusion and sharpening near shock solutions the ellam methodology employs space time finite elements with edges oriented along flow paths and space time test functions that satisfy a local adjoint condition this combination extends eulerian lagrangian concepts in a systematic mass conservative fashion to problems with general boundary conditions various kinds of boundary conditions are considered and a local time stepping procedure is developed for a no flow outlet condition that leads to a boundary layer numerical experiments illustrate the potential of these methods

numerical simulation of hydrogen dispersion behaviour in a partially open space by a stabilized balancing domain decomposition method the dispersion behaviour of leaking hydrogen in a partially open space is simulated numerically by a balancing domain decomposition method in this work an analogy of the thermal convection problems is applied the linear systems of navier stokes equations and the convection diffusion equation are symmetrized by a pressure stabilized domain decomposition method the interface problem after domain decomposition is solved by a balancing preconditioned conjugate gradient method numerical results are validated by comparing with the experimental data and available numerical results the transient behaviour of hydrogen dispersion and accumulation in the partially open space is discussed the mechanism of air influence is investigated and safe region inside this partially open space is classified

spatial filter averaging approach of probabilistic method to linear second order partial differential equations of the parabolic type a backward in time probabilistic method with spatial filter averaging is presented to solve linear second order partial differential equations of the parabolic type an advantage of this methodology is that while forward methods are subject to region with loss of density of particles and hence loss of spatial resolution of the solution the solution given by backward methods is given on any desired grid however traditional backward time probabilistic method using monte carlo averaging are computationally expensive we prove a convergence result and present several examples the method leads to important improvement in computational efficiency and is expected to perform well to solve high dimensional problems where a solution is needed on a large grid

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

a comparison of methods for testing homogeneity of proportions in teratologic studies summary we consider teratologic studies in which the aim is to compare the survival rate of animals in a treatment group to the corresponding rate in a control group the design of such studies often involves the allocation of intact litters of animals to treatment invalidating the application of standard statistical methods we review the strengths and weaknesses of several approaches for dealing with this problem including methodology recently developed for the analysis of clustered binary data a simulation study is conducted in which litter sizes are generated from a distribution having specified mean and degree of imbalance it is recommended on the basis of this study and on theoretical considerations that the choice of method should depend on whether the comparison of interest is experimental or observational for experimental comparisons involving the random assignment of litters to different treatment groups methods based on the adjustment of standard chi square statistics are recommended unless the number of litters in each group is very large

from finite differences to finite elements a short history of numerical analysis of partial differential equations abstract this is an account of the history of numerical analysis of partial differential equations starting with the 1928 paper of courant friedrichs and lewy and proceeding with the development of first finite difference and then finite element methods the emphasis is on mathematical aspects such as stability and convergence analysis