locally discontinuous but globally continuous galerkin methods for elliptic problems abstract we propose and analyze a stabilized hybrid finite element method for elliptic problems consisting of locally discontinuous galerkin problems in the primal variable coupled to a globally continuous problem in the multiplier numerical analysis shows that the proposed formulation preserves the main properties of the associate dg method such as consistency stability boundedness and optimal rates of convergence in the energy norm and in the l 2 norm for adjoint consistent formulations for using an element based data structure it has basically the same complexity and computational cost of classical conforming finite element methods convergence studies confirm the optimal rates of convergence predicted by the numerical analysis presented here with accuracy equivalent or even better than the corresponding dg approximations

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

analysis of a semidiscrete discontinuous galerkin scheme for compressible miscible displacement problem numerical approximation of the coupled system of compressible miscible displacement problem in porous media is considered in this paper a continuous in time discontinuous galerkin scheme is developed the symmetric interior penalty discontinuous galerkin method is used to solve both the flow and transport equations upwind technique is used to treat the convection term in the transport equation the hp a priori error bounds are derived

subgrid stabilized defect correction method for a steady state natural convection problem in this paper we consider a subgrid stabilized defect correction method for the steady state natural convection problem we state the stabilities and error results for the defect step and the first correction step of the defect correction method the derived theoretical results are supported by several numerical examples

singularly perturbed volterra integral equations ii a formal methodology is developed to obtain a uniformly valid asymptotic solution to a class of singularly perturbed volterra integral equations the methodology systematically determines the appropriate integral equations which govern the inner and outer solutions at each order of the perturbation analysis several examples are presented to illustrate the procedure

interior penalty variational multiscale method for the incompressible navier stokes equation monitoring artificial dissipation in this paper we apply the interior penalty method analyzed in e burman and m a fernndez numer math 107 2007 no 1 39 77 mr2317827 2008c 65317 to flows at high reynolds number as a possible measure of solution quality we propose to monitor the ratio between the artificial dissipation induced by the numerical method and the computed physical dissipation for smooth flows we prove that for our method the artificial dissipation serves as an a posteriori error estimator and also that it vanishes at an optimal rate in the case of flows with multiscale features we discuss a heuristic approach relating the decay of the artificial dissipation to the decay rate of the power spectrum some numerical results in two space dimensions are presented examining the relation between the numerical dissipation and solution quality

a non conforming piecewise quadratic finite element on triangles it is shown in this paper that non conforming finite elements on the triangle using second degree polynomials can be easily built and used indeed they appear as an enriched version of the standard piecewise quadratic six node element this work is divided into two parts in the first we present the basic properties of the element namely how it can be built and basic error estimates we also show that this element exhibits a very peculiar regularity property in the second part we apply our element to the approximation of viscous incompressible flows and more generally to the approximation of incompressible materials

a two level variational multiscale method for convection dominated convection diffusion equations this paper studies the error in the efficient implementation of and time stepping methods for a variational multiscale method vms for solving convection dominated problems the vms studied uses a fine mesh c0 finite element space xh to approximate the concentration and a coarse mesh discontinuous vector finite element space lh for the large scales of the flux in the two scale discretization our tests show that these choices lead to an efficient vms whose complexity is further reduced if a locally l2 orthogonal basis for lh is used a fully implicit and a semi implicit treatment of the terms which link effects across scales are tested and compared the semi implicit vms was much more efficient the observed global accuracy of the most straightforward vms implementation was much better than the artificial diffusion stabilization and comparable to a streamline diffusion finite element method in our tests

generalized mantel haenszel estimators for k 2 x j tables mickey and elashoff 1985 biometrics 41 623 635 gave an extension of mantel haenszel estimation to log linear models for 2 x j x k tables their extension yields two generalizations of the mantel haenszel odds ratio estimator to k 2 x j tables this paper provides variance and covariance estimators for these generalized mantel haenszel estimators that are dually consistent i e consistent in both large strata and sparse data and presents comparisons of the efficiency of the generalized mantel haenszel estimators

subgrid stabilized defect correction methods for the navier stokes equations we consider the synthesis of a recent subgrid stabilization method with defect correction methods the combination is particularly efficient and combines the best algorithmic features of each we prove convergence of the method for a fixed number of corrections as the mesh size goes to zero and derive parameter scalings from the analysis we also present some numerical tests which both verify the theoretical predictions and illustrate the method s promise

discontinuous subgrid formulations for transport problems in this paper we develop two discontinuous galerkin formulations within the framework of the two scale subgrid method for solving advection diffusion reaction equations we reformulate using broken spaces the nonlinear subgrid scale nsgs finite element model in which a nonlinear eddy viscosity term is introduced only to the subgrid scales of a finite element mesh here two new subgrid formulations are built by introducing subgrid stabilized terms either at the element level or on the edges by means of the residual of the approximated resolved scale solution inside each element and the jump of the subgrid solution across interelement edges the amount of subgrid viscosity is scaled by the resolved scale solution at the element level yielding a self adaptive method so that no additional stabilization parameter is required numerical experiments are conducted in order to demonstrate the behavior of the proposed methodology in comparison with some discontinuous galerkin methods

gb splines of arbitrary order explicit formulae and recurrence relations for the calculation of generalized b splines gb splines of arbitrary order are given we derive main properties of gb splines and their series i e partition of unity shape preserving properties invariance with respect to ane transformations etc it is shown that such splines have the variation diminishing property and are chebyshevian splines c 1999 elsevier science b v all rights reserved

a connection between subgrid scale eddy viscosity and mixed methods we consider a new mixed method related to the evss method in computational viscoelasticity for the convection dominated convection diffusion equation in which stabilization is added then removed through the extra mixed variables this consistent stabilization is equivalent to an artificial viscosity operator acting only on the fluctuations in u h by suitable choice of the mixed spaces a method of guermond is recovered exactly we show that for a different natural choice a new method results with global error estimates similar to both guermond s method and the streamline diffusion supg method

an energy and helicity conserving finite element scheme for the navier stokes equations we present a new finite element scheme for solving the navier stokes equations that exactly conserves both energy int omega u 2 and helicity int omega u cdot nabla times u in the absence of viscosity and external force we prove stability exact conservation and convergence for the scheme energy and helicity are exactly conserved by using a combination of the usual convective form with the rotational form of the nonlinearity and solving for both velocity and a projected vorticity in a trapezoidal time discretization numerical results are presented that compare the scheme to the usual trapezoidal schemes

a fourth second order accurate collocation method for singularly perturbed two point boundary value problems using tension splines the collocation tension spline is considered as a numerical solution of a singularly perturbed two point boundary value problem varepsilon y b y c y f the collocation points are chosen as a generalization of the classical gaussian points unlike the traditional approach we employ the b spline representation in the analysis this leads to global quadratic convergence of the method for small perturbation parameters and for large values the order of convergence is four

a discontinuous subgrid eddy viscosity method for the time dependent navier stokes equations in this paper we provide an error analysis of a subgrid scale eddy viscosity method using discontinuous polynomial approximations for the numerical solution of the incompressible navier stokes equations optimal continuous in time error estimates of the velocity are derived the analysis is completed with some error estimates for two fully discrete schemes which are first and second order in time respectively

discontinuous finite element methods for incompressible flows on subdomains with non matching interfaces abstract in this paper an improved inf sup condition is derived for a class of discontinuous galerkin methods for solving the steady state incompressible stokes and navier stokes equations the computational domain is subdivided into subdomains with non matching meshes at the interfaces optimal error estimates are obtained numerical experiments including two benchmark problems are presented

testing the conditional independence and monotonicity assumptions of item response theory when item characteristic curves are nondecreasing functions of a latent variable the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses this general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves the proposed tests are simple have known asymptotic null distributions and possess certain optimal properties in an example the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves

a discontinuous galerkin method with nonoverlapping domain decomposition for the stokes and navier stokes problems a family of discontinuous galerkin finite element methods is formulated and analyzed for stokes and navier stokes problems an inf sup condition is established as well as optimal energy estimates for the velocity and l 2 estimates for the pressure in addition it is shown that the method can treat a finite number of nonoverlapping domains with nonmatching grids at interfaces

finite element approximations of the nonstationary navier stokes problem part iv error estimates for second order time discretization this paper provides an error analysis for the crank nicolson method of time discretization applied to spatially discrete galerkin approximations of the nonstationary navier stokes equations second order error estimates are proven locally in time under realistic assumptions about the regularity of the solution for approximations of an exponentially stable solution these local error estimates are extended uniformly in time as text t to infty

stabilized finite element methods for the generalized oseen problem the numerical solution of the non stationary incompressible navierstokes model can be split into linearized auxiliary problems of oseen type we present in a unique way different stabilization techniques of finite element schemes on isotropic meshes first we describe the state of the art for the classical residual based supg pspg method then we discuss recent symmetric stabilization techniques which avoid some drawbacks of the classical method these methods are closely related to the concept of variational multiscale methods which seems to provide a new approach to large eddy simulation finally we give a critical comparison of these methods

nonconforming finite elements for the stokes problem on obtient un nouveau resultat de stabilite pour l approximation du probleme de stokes stationnaire avec des elements finis non conformes

generalization of the mantel haenszel estimating function for sparse clustered binary data we extend the mantel haenszel estimating function to estimate both the intra cluster pairwise correlation and the main effects for sparse clustered binary data we propose both a composite likelihood approach and an estimating function approach for the analysis of such data the proposed estimators are consistent and asymptotically normally distributed simulation results demonstrate that the two approaches are comparable in terms of bias and efficiency however the estimating equation approach is computationally simpler analysis of the georgia high blood pressure survey is used for illustration

uniform difference method for singularly perturbed volterra integro differential equations singularly perturbed volterra integro differential equations is considered an exponentially fitted difference scheme is constructed in a uniform mesh which gives first order uniform convergence in the discrete maximum norm numerical experiments support the theoretical results

tension spline collocation methods for singularly perturbed volterra integro differential and volterra integral equations we consider the numerical discretization of singularly perturbed volterra integro differential equations vide y t q1 t q2 t y t 0t k t s y s ds t i 0 t y 0 y0 and volterra integral equations vie y t g t 0t k t s y s ds t i by tension spline collocation methods in certain tension spline spaces where is a small parameter satisfying 0 1 and ql q2 g and k are functions sufficiently smooth on their domains to ensure that eqs and posses a unique solution we give an analysis of the global convergence properties of a new tension spline collocation solution for 0 1 for singularly perturbed vide and vie thus extending the existing theory for 1 to the singularly perturbed case

a mixed discontinuous galerkin method with symmetric stress for brinkman problem based on the velocity pseudostress formulation abstract the brinkman equations can be regarded as a combination of the stokes and darcy equations which model transitions between the fast flow in channels governed by stokes equations and the slow flow in porous media governed by darcy s law the numerical challenge for this model is the designing of a numerical scheme which is stable for both the stokes dominated high permeability and the darcy dominated low permeability equations in this paper we solve the brinkman model in n dimensions n 2 3 by using the mixed discontinuous galerkin mdg method which meets this challenge this mdg method is based on the pseudostress velocity formulation and uses a discontinuous piecewise polynomial pair p k 1 s p k k 0 where the stress field is symmetric the main unknowns are the pseudostress and the velocity whereas the pressure is easily recovered through a simple postprocessing a key step in the analysis is to establish the parameter robust inf sup stability through specific parameter dependent norms at both continuous and discrete levels therefore the stability results presented here are uniform with respect to the permeability thanks to the parameter robust stability analysis we obtain optimal error estimates for the stress in broken h div norm and velocity in l 2 norm furthermore the l 2 error estimate for pseudostress is derived under certain conditions finally numerical experiments are provided to support the theoretical results and to show the robustness accuracy and flexibility of the mdg method

projection method mantel haenszel estimator for k 2 j tables abstract a projection method is introduced to generalize the mantel haenszel estimator for estimating the common odds ratios in k 2 j j 2 tables the method provides estimators in an explicit form and needs no iterative computation it is shown that the generalized mantel haenszel estimator proposed by greenland and yanagawa and fujii is obtained by this method as a special case furthermore selecting appropriate weight it is shown that the method leads to an estimator that is asymptotically equivalent to the generalized mantel haenszel estimator proposed by liang a dually consistent estimator of the variance of the estimator is proposed the characteristics of these estimators have been evaluated by monte carlo means

sharp error bounds for interpolating splines in tension abstract sharp error bounds for interpolating splines in tension with variable tension parameters are considered error bounds given are the best possible ones in the limit case of the tension parameter p that is for linear p and cubic p 0 spline error bounds sharper than those previously published are also developed for derivatives

on the numerical solution of linear and nonlinear volterra integral and integro differential equations abstract sinc bases are developed to approximate the solutions of linear and nonlinear volterra integral and integro differential equations properties of these sinc bases and some operational matrices are first presented these properties are then used to reduce the integral and integro differential equations to systems of linear or nonlinear algebraic equations numerical examples illustrate the pertinent features of the method and its applicability to a large variety of problems the examples include convolution type singular as well as singularly perturbed problems

a finite element variational multiscale method for the navier stokes equations this paper presents a variational multiscale method vms for the incompressible navier stokes equations which is defined by a large scale space lh for the velocity deformation tensor and a turbulent viscosity nu t the connection of this method to the standard formulation of a vms is explained the conditions on lh under which the vms can be implemented easily and efficiently into an existing finite element code for solving the navier stokes equations are studied numerical tests with the smagorinsky large eddy simulation model for nu t are presented

piecewise quasilinearization techniques for singularly perturbed volterra integro differential equations abstract three families of iterative quasilinear methods for the numerical solution of singularly perturbed volterra integro differential equations are presented two of these methods are based on the piecewise integration of the differential equations and the use of quadrature rules while the third one employs a locally frozen approximation for the coefficients and right hand side of the differential equation it is shown that these quasilinear methods are first order accurate for step sizes equal to or larger than the initial layer thickness and are less accurate than exponentially fitted techniques whose coefficients are selected so that the finite difference equations have truncation errors of second and third order even though they exhibit only first order accuracy for initial layer thicknesses equal to or smaller than the step size it is also shown that the quasilinear methods presented in this paper are of exponential type and provide more accurate results than the backward euler and trapezoidal methods for step sizes larger than the initial layer thickness and the quasilinear frozen method is less accurate than quasilinear techniques that make use of an integrating factor and numerical quadratures

extended mantel haenszel estimating procedure for multivariate logistic regression models a class of estimating functions is proposed for the estimation of multivariate relative risk in stratified case control studies it reduces to the well known mantel haenszel estimator when there is a single binary risk factor large sample properties of the solutions to the proposed estimating equations are established for two distinct situations efficiency calculations suggest that the proposed estimators are nearly fully efficient relative to the conditional maximum likelihood estimator for the parameters considered application of the proposed method to family data and longitudinal data where the conditional likelihood approach fails is discussed two examples from case control studies and one example from a study on familial aggregation are presented

analysis of the spectral vanishing viscosity method for periodic conservation laws the convergence of the spectral vanishing method for both the spectral and pseudospectral discretizations of the inviscid burgers equation is analyzed it is proved that this kind of vanishing viscosity is responsible for spectral decay of those fourier coefficients located toward the end of the computed spectrum consequently the discretization error is shown to be spectrally small independently of whether or not the underlying solution is smooth this in turn implies that the numerical solution remains uniformly bounded and convergence follows by compensated compactness arguments

estimation of penalty parameters for symmetric interior penalty galerkin methods this paper presents computable lower bounds of the penalty parameters for stable and convergent symmetric interior penalty galerkin methods in particular we derive the explicit dependence of the coercivity constants with respect to the polynomial degree and the angles of the mesh elements numerical examples in all dimensions and for different polynomial degrees are presented we show the numerical effects of loss of coercivity

numerical analysis of the unconditionally stable discontinuous galerkin schemes for the nonstationary conduction convection problem abstract this work aims at employing the discontinuous galerkin dg methods for solving the nonstationary conduction convection model which is motivated by advantages of dg methods the discontinuous element pair p k p k 1 p k in the space discretization and backward euler scheme in time are applied as well as an explicit upwind scheme based on picard iteration is introduced for the coupled term existence and uniqueness of the approximation solutions are proved along with preserving the unconditional stability of the numerical schemes the priori error estimates for velocity pressure and temperature are also derived numerical tests are provided to verify the theoretical analysis and to indicate the efficiency of the dg methods in simulating practical problems