a multiscale direct solver for the approximation of flows in high contrast porous media abstract we consider a non overlapping domain decomposition approach to approximate the solution of elliptic boundary value problems with high contrast in their coefficients we propose a method such that initially local solutions subject to robin boundary conditions in each primal subdomain are constructed with locally conservative finite element or finite volume methods then a novel approach is introduced to obtain a discontinuous global solution in terms of linear combination of the local subdomain solutions in the proposed algorithm the computation of local solutions for unions of subdomains are localized at nearest neighbor subdomain boundaries thus avoiding the solution of global interface problems we remove discontinuities in a smoothing step that is defined on a staggered grid or dual subdomains the resulting algorithm is naturally parallelizable and can be employed as a parallel direct solver offering great potential for the numerical solution of large problems in fact subdomains can be considered small enough to fit well in gpus and the proposed procedure can handle adaptive in space simulations effectively numerical simulations are presented and discussed we demonstrate the effectiveness of the proposed approach with two and three dimensional high contrast and channelized coefficients that lead to challenging approximation problems the new procedure although designed for parallel processing is also of value for serial calculations

some least squares galerkin procedures for first order time dependent convection diffusion system abstract four least squares galerkin finite element schemes are formulated to solve first order time dependent convection diffusion systems and the convergence of these schemes is analyzed

domain decomposition algorithms for mixed methods for second order elliptic problems domain decomposition algorithms for mixed finite element methods for linear second order elliptic problems in r 2 and r 3 are developed a convergence theory for two level and multilevel schwarz methods applied to the algorithms under consideration is given it is shown that the condition number of these iterative methods is bounded uniformly from above in the same manner as in the theory of domain decomposition methods for conforming and nonconforming finite element methods for the same differential problems numerical experiments are presented to illustrate the present techniques

on mixed finite element methods for linear elastodynamics we construct and analyze finite element methods for approximating the equations of linear elastodynamics using mixed elements for the discretization of the spatial variables we consider two different mixed formulations for the problem and analyze semidiscrete and up to fourth order in time fully discrete approximations l 2 optimal order error estimates are proved for the approximations of displacement and stress

on the use of rational iterations and domain decomposition methods for the helmholtz problem an iterative algorithm for the numerical solution of the helmholtz problem is considered it is difficult to solve the problem numerically in particular when the imaginary part of the wave number is zero or small we develop a parallel iterative algorithm based on a rational iteration and a nonoverlapping domain decomposition method for such a non hermitian non coercive problem algorithm parameters artificial damping and relaxation are introduced to accelerate the convergence speed of the iteration convergence analysis and effective strategies for finding efficient algorithm parameters are presented numerical results carried out on an ncube2 are given to show the efficiency of the algorithm to reduce the boundary reflection we employ a hybrid absorbing boundary condition abc which combines the first order abc and the physical q abc computational results comparing the hybrid abc with non hybrid ones are presented

a stabilized mixed finite element method for darcy flow we develop new stabilized mixed finite element methods for darcy flow stability and an a priori error estimate in the stability norm are established a wide variety of convergent finite elements present themselves unlike the classical galerkin formulation which requires highly specialized elements an interesting feature of the formulation is that there are no mesh dependent parameters numerical tests confirm the theoretical results 2002 elsevier science b v all rights reserved

on the preservation of log convexity and log concavity under some classical bernstein type operators this paper analyzes the preservation of both the log convexity and the log concavity under certain bernstein type operators some results are provided for the bernstein szasz baskakov the gamma type and the weierstrass operators probabilistic methods support the proofs of these results

a parallel domain decomposition algorithm of mixed element equation for second order elliptic dirichlet boundary value problem a parallel domain decomposition algorithm of schwarz type is introduced to solve the mixed finite element equation for the dirichlet boundary value problem of a second order partial differential equation of elliptic type and convergence of this algorithm is analyzed

a discrete differential sequence for elasticity based upon continuous displacements the present paper introduces a mixed stress displacement method for linear elasticity as an extension of the work performed by christiansen numer math 119 2011 pp 613 640 for computational relativity moreover we establish self adjointness in a special sense and perform numerical simulations to assess the relevance of the method including comparison with the recent tdnns a sinwel a new family of mixed finite elements for elasticity ph d thesis linz university 2009 a pechstein and j schoberl math models methods appl sci 21 2011 pp 1761 1782 mixed formulation extensions to higher order approximations and nonlinear elasticity are also introduced

energy norm a posteriori error estimates for mixed finite element methods this paper deals with the a posteriori error analysis of mixed finite element methods for second order elliptic equations it is shown that a reliable and efficient error estimator can be constructed using a postprocessed solution of the method the analysis is performed in two different ways under a saturation assumption and using a helmholtz decomposition for vector fields

analysis of mixed finite element methods on locally refined grids we consider the mixed finite element method for locally refined triangulations a local projection operator hat pi h is defined to satisfy the commutation property that is required in the general theory of mixed methods our results can be applied to every known space of arbitrary order over rectangles or triangles optimal order error estimates and superconvergence for the flux along the gauss lines are established

mixed finite elements for second order elliptic problems in three variables two families of mixed finite elements one based on simplices and the other on cubes are introduced as alternatives to the usual raviart thomas nedelec spaces these spaces are analogues of those introduced by brezzi douglas and marini in two space variables error estimates inl2 andh s are derived

on uniform approximation by some classical bernstein type operators abstract we investigate the functions for which certain classical families of operators of probabilistic type over noncompact intervals provide uniform approximation on the whole interval the discussed examples include the szasz operators the szasz durrmeyer operators the gamma operators the baskakov operators and the meyer konig and zeller operators we show that some results of totik remain valid for unbounded functions at the same time that we give simple rates of convergence in terms of the usual modulus of continuity we also show by a counterexample that the result for meyer konig and zeller operators does not extend to cheney and sharma operators

the multiscale robin coupled method for flows in porous media abstract a multiscale mixed method aiming at the accurate approximation of velocity and pressure fields in heterogeneous porous media is proposed the procedure is based on a new domain decomposition method in which the local problems are subject to robin boundary conditions the domain decomposition procedure is defined in terms of two independent spaces on the skeleton of the decomposition corresponding to interface pressures and fluxes that can be chosen with great flexibility to accommodate local features of the underlying permeability fields the well posedness of the new domain decomposition procedure is established and its connection with the method of douglas et al 1993 12 is identified also allowing us to reinterpret the known procedure as an optimized schwarz or two lagrange multiplier method the multiscale property of the new domain decomposition method is indicated and its relation with the multiscale mortar mixed finite element method mmmfem and the multiscale hybrid mixed mhm finite element method is discussed numerical simulations are presented aiming at illustrating several features of the new method initially we illustrate the possibility of switching from mmmfem to mhm by suitably varying the robin condition parameter in the new multiscale method then we turn our attention to realistic flows in high contrast channelized porous formations we show that for a range of values of the robin condition parameter our method provides better approximations for pressure and velocity than those computed with either the mmmfem and the mhm this is an indication that our method has the potential to produce more accurate velocity fields in the presence of rough realistic permeability fields of petroleum reservoirs

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

a multiscale preconditioner for stochastic mortar mixed finite elements the aim of this paper is to introduce a new approach to efficiently solve sequences of problems that typically arise when modeling flow in stochastic porous media the governing equations are based on darcy s law with a stochastic permeability field starting from a specified covariance relationship the log permeability is decomposed using a truncated karhunen loeve expansion multiscale mortar mixed finite element approximations are used in the spatial domain and a nonintrusive sampling method is used in the stochastic dimensions a multiscale mortar flux basis is computed for a single permeability called a training permeability that captures the main characteristics of the porous media and is used as a preconditioner for each stochastic realization we prove that the condition number of the preconditioned interface operator is independent of the subdomain mesh size and the mortar mesh size computational results confirm that our approach provides an efficient means to quantify the uncertainty for stochastic flow in porous media

super convergence and post processing for mixed finite element approximations of the wave equation we consider the numerical approximation of acoustic wave propagation problems by mixed text bdm k 1 text p k finite elements on unstructured meshes optimal convergence of the discrete velocity and super convergence of the pressure are established based on these results we propose a post processing strategy that allows us to construct an improved pressure approximation from the numerical solution corresponding results are well known for mixed finite element approximations of elliptic problems and we extend these analyses here to the hyperbolic problem under consideration we also consider the subsequent time discretization by the crank nicolson method and show that the analysis and the post processing strategy can be generalized to the fully discrete schemes our proofs do not rely on duality arguments or inverse inequalities and the results therefore also apply for non convex domains and non uniform meshes

degenerate two phase incompressible flow iii sharp error estimates this is the third paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic parabolic partial differential system which describes the flow of two incompressible immiscible fluids in porous media in this paper we consider a finite element approximation for this system the elliptic equation for the pressure and velocity is approximated by a mixed finite element method while the degenerate parabolic equation for the saturation is approximated by a galerkin finite element method a fully discrete approximation is analyzed sharp error estimates in energy norms are obtained for this approximation the error analysis does not use any regularization of the saturation equation the error estimates are derived directly from the degenerate equation also the analysis does not impose any restriction on the nature of degeneracy finally it respects the minimal regularity on the solution of the differential system

mixed finite element methods on nonmatching multiblock grids we consider mixed finite element methods for second order elliptic equations on nonmatching multiblock grids a mortar finite element space is introduced on the nonmatching interfaces we approximate in this mortar space the trace of the solution and we impose weakly a continuity of flux condition a standard mixed finite element method is used within the blocks optimal order convergence is shown for both the solution and its flux moreover at certain discrete points superconvergence is obtained for the solution and also for the flux in special cases computational results using an efficient parallel domain decomposition algorithm are presented in confirmation of the theory

a multiscale fixed stress split iterative scheme for coupled flow and poromechanics in deep subsurface reservoirs abstract in coupled flow and poromechanics phenomena representing hydrocarbon production or co 2 sequestration in deep subsurface reservoirs the spatial domain in which fluid flow occurs is usually much smaller than the spatial domain over which significant deformation occurs the typical approach is to either impose an overburden pressure directly on the reservoir thus treating it as a coupled problem domain or to model flow on a huge domain with zero permeability cells to mimic the no flow boundary condition on the interface of the reservoir and the surrounding rock the former approach precludes a study of land subsidence or uplift and further does not mimic the true effect of the overburden on stress sensitive reservoirs whereas the latter approach has huge computational costs in order to address these challenges we augment the fixed stress split iterative scheme with upscaling and downscaling operators to enable modeling flow and mechanics on overlapping nonmatching hexahedral grids flow is solved on a finer mesh using a multipoint flux mixed finite element method and mechanics is solved on a coarse mesh using a conforming galerkin method the multiscale operators are constructed using a procedure that involves singular value decompositions a surface intersections algorithm and delaunay triangulations we numerically demonstrate the convergence of the augmented scheme using the classical mandel s problem solution

a mixed method for the biharmonic problem based on a system of first order equations we introduce a new mixed method for the biharmonic problem the method is based on a formulation where the biharmonic problem is rewritten as a system of four first order equations a hybrid form of the method is introduced which allows us to reduce the globally coupled degrees of freedom to only those associated with lagrange multipliers which approximate the solution and its derivative at the faces of the triangulation for k ge 1 a projection of the primal variable error superconverges with order k 3 while the error itself converges with order k 1 only this fact is exploited by using local postprocessing techniques that produce new approximations to the primal variable converging with order k 3 we provide numerical experiments that validate our theoretical results

on an approximation process of integral type abstract in this paper we study a class of integral type positive linear operators depending on a parameter 0 1 approximation properties of this class are explored the rate of convergence in terms of the usual moduli of smoothness is given the uniform approximation over unbounded intervals is established the convergence in certain weighted spaces is investigated for particular case 0 some previous results are recaptured

a family of rectangular mixed elements with a continuous flux for second order elliptic problems we present a family of mixed finite element spaces for second order elliptic equations in two and three space dimensions our spaces approximate the vector flux by a continuous function our spaces generalize certain spaces used for approximation of stokes problems the finite element method incorporates projections of the dirichlet data and certain low order terms the method is locally conservative on the average suboptimal convergence is proven and demonstrated numerically the key result is to construct a flux pi projection operator that is bounded in the sobolev space h1 preserves a projection of the divergence and approximates optimally moreover the corresponding raviart thomas flux preserving pi projection operator is an l2 projection when restricted to this family of spaces

variances for maximum penalized likelihood estimates obtained via the em algorithm we address the problem of providing variances for parameter estimates obtained under a penalized likelihood formulation through use of the em algorithm the solution proposed represents a synthesis of two existent techniques firstly we exploit the supplemented em algorithm developed by meng and rubin that provides variance estimates for maximum likelihood estimates obtained via the em algorithm their procedure relies on evaluating the jacobian of the mapping induced by the em algorithm secondly we utilize results from green that provide expressions for jacobians of mappings induced by em algorithms applied to a penalized likelihood the resultant procedure requires no more code than that needed for the penalized em algorithm itself

domain decomposition iterative procedures for solving scalar waves in the frequency domain the propagation of dispersive waves can be modeled relevantly in the frequency domain a wave problem in the frequency domain is difficult to solve numerically in addition to having a complex valued solution the problem is neither hermitian symmetric nor coercive in a wide range of applications in geophysics or quantum mechanics in this paper we consider a parallel domain decomposition iterative procedure for solving the problem by finite differences or conforming finite element methods the analysis includes the decomposition of the domain into either the individual elements or larger subdomains blocks of finite elements to accelerate the speed of convergence we introduce relaxation parameters on the subdomain interfaces and an artificial damping iteration the convergence rate of the resulting algorithm turns out to be independent on the mesh size and the wave number numerical results carried out on an ncube2 parallel computer are presented to show the effectiveness of the method

on use of the em algorithm for penalized likelihood estimation summary the em algorithm is a popular approach to maximum likelihood estimation but has not been much used for penalized likelihood or maximum a posteriori estimation this paper discusses properties of the em algorithm in such contexts concentrating on rates of conver gence and presents an alternative that is usually more practical and converges at least as quickly the em algorithm is a general approach to maximum likelihood estimation rather than a specific algorithm dempster et al 1977 discussed the method and derived basic properties demonstrating that a variety of procedures previously developed rather informally could be unified the common strand to problems where the approach is applicable is a notion of incomplete data this includes the conventional sense of missing data but is much broader than that the em algorithm demon strates its strength in situations where some hypothetical experiment yields data from which estimation is particularly convenient and economical the incomplete data actually at hand are regarded as observable functions of these complete data the resulting algorithms while usually slow to converge are often extremely simple and remain practical in large problems where no other approaches may be feasible dempster et al 1977 briefly refer to the use of the same approach to the problem of finding the posterior mode maximum a posteriori estimate in a bayesian estima

stochastic collocation and mixed finite elements for flow in porous media the aim of this paper is to quantify uncertainty of flow in porous media through stochastic modeling and computation of statistical moments the governing equations are based on darcy s law with stochastic permeability starting from a specified covariance relationship the log permeability is decomposed using a truncated karhunen loeve expansion mixed finite element approximations are used in the spatial domain and collocation at the zeros of tensor product hermite polynomials is used in the stochastic dimensions error analysis is performed and experimentally verified with numerical simulations computational results include incompressible and slightly compressible single and two phase flow

global estimates for mixed methods for second order elliptic equations global error estimates in l2 92 l 9 and h s q 2 in r2 or a re derived for a mixed finite element method for the dirichlet problem for the elliptic operator lp div a grad p bp cp based on the raviart thomas nedelec space vh x wh c h div 92 x l2 g2 optimal order estimates are obtained for the approximation of p and the associated velocity field u a grad p bp in l2 g2 and h s 92 0 6 s k 1 and if q c r2 forp in lv2

a constructive method for deriving finite elements of nodal type in this paper we propose an algorithm to derive nodal methods corresponding to various two and three dimensional nonconforming and mixed finite elements we show that this algorithm can be used to obtain several classical schemes as well as some more recently developed schemes and that it leads to a simple proof of unisolvence for these methods finally we use our method to obtain a three dimensional nodal scheme of bdm type

a method for assessing age time disease incidence using serial prevalence data summary this paper considers nonparametric estimation of age and time specific trends in disease incidence using serial prevalence data collected from multiple cross sectional samples of a population over time the methodology accounts for differential selection of diseased and undiseased individuals resulting for example from differences in mortality it is shown that when a log linear incidence odds model is adopted an em algorithm provides a convenient method for carrying out maximum likelihood estimation primarily using existing generalized linear models software the procedure is quite general allowing a range of age time incidence models to be fitted under the same framework furthermore by making use of existing software for fitting generalized additive models the procedure can be generalized with virtually no extra complexity to allow maximization of a penalized likelihood for smooth nonparametric estimation automatic choice of smoothing level for the penalized likelihood estimates is discussed using generalized cross validation the method is applied to a data set on serial toxoplasmosis prevalence which has previously been analyzed under the assumption of nondifferential selection a variety of age time incidence models are fitted and the sensitivity to plausible differential selection patterns is considered it is found that nonmultiplicative models are unnecessary and that qualitative incidence trends are fairly robust to differential selection

mixed approximation of a population diffusion equation abstract a numerical method is proposed to approximate the solution of a nonlinear and nonlocal system of integro differential equations describing age dependent population dynamics with spatial diffusion a finite difference method along the characteristic age time direction combined with mixed finite elements in the spatial variable is used for the approximation optimal order error estimates are derived for the relevant variables using nonnegativity of the discrete solution a stability of the method is also proved

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

finite element methods for the simulation of waves in composite saturated poroviscoelastic media this work presents and analyzes a collection of finite element procedures for the simulation of wave propagation in a porous medium composed of two weakly coupled solids saturated by a single phase fluid the equations of motion formulated in the space frequency domain include dissipation due to viscous interaction between the fluid and solid phases with a correction factor in the high frequency range and intrinsic anelasticity of the solids modeled using linear viscoelasticity this formulation leads to the solution of a helmholtz type boundary value problem for each temporal frequency for the spatial discretization nonconforming finite element spaces are employed for the solid phases while for the fluid phase the vector part of the raviart thomas nedelec mixed finite element space is used optimal a priori error estimates for global standard and hybridized galerkin finite element procedures are derived an iterative nonoverlapping domain decomposition procedure is also presented and convergence results are derived numerical experiments showing the application of the numerical procedures to simulate wave propagation in partially frozen porous media are presented

on the cheney and sharma operator abstract in this paper we consider the double indexed bernstein power series operator p a t introduced by cheney and sharma and related to the classical laguerre polynomials we obtain sharp estimates of the first two moments which allow us to prove that when acting on a continuous function f the convergence of p a t f to f is uniform on the whole interval 0 1 moreover we show that the rates of convergence depend on the way in which t a goes to 0 we also show that p a t preserves monotonicity and global smoothness finally we consider the monotonicity properties of p a t with respect to both parameters to achieve the mentioned results we use a probabilistic approach based on the representation of the operator in terms of a suitable multi indexed stochastic process the path properties and the martingale type properties of this process are key points to give short proofs

an optimal parallel nonoverlapping domain decomposition iterative procedure a nonoverlapping domain decomposition iterative procedure is developed and analyzed for second order elliptic problems in mathbb r n its convergence is proved the method is based on a robin type consistency condition with two parameters called a transmission coefficient and a penalty coefficient as a transmission condition together with a derivative free transmission data updating technique on the artificial interfaces then the method is applied to the nonconforming finite element problems a nonoverlapping domain decomposition iterative procedure for solving the nonconforming finite element problems of second order partial differential equations is developed and analyzed which is directly presented to the nonconforming finite element problems without introducing any lagrange multipliers its convergence is demonstrated and the convergence rate is derived the convergence analyses imply that the convergence rate is independent of the finite element meshes size while choosing the right parameters furthermore the conclusions are extended to the unstructured finite element meshes for both continuous problems and discrete problems the method of this paper can be applied to general multisubdomain decompositions and implemented on parallel machines with local communications naturally the method also allows choosing subdomains very flexibly even as small as an individual element for finite element problems

fully discrete finite element analysis of multiphase flow in groundwater hydrology this paper deals with the development and analysis of a fully discrete finite element method for a nonlinear differential system for describing an air water system in groundwater hydrology the nonlinear system is written in a fractional flow formulation i e in terms of a saturation and a global pressure the saturation equation is approximated by a finite element method while the pressure equation is treated by a mixed finite element method the analysis is carried out first for the case where the capillary diffusion coefficient is assumed to be uniformly positive and is then extended to a degenerate case where the diffusion coefficient can be zero it is shown that error estimates of optimal order in the l 2 norm and almost optimal order in the l infty norm can be obtained in the nondegenerate case in the degenerate case we consider a regularization of the saturation equation by perturbing the diffusion coefficient the norm of error estimates depends on the severity of the degeneracy in diffusivity with almost optimal order convergence for nonsevere degeneracy implementation of the fractional flow formulation with various nonhomogeneous boundary conditions is also discussed results of numerical experiments using the present approach for modeling groundwater flow in porous media are reported

bernstein durrmeyer operators abstract in this paper we consider the durrmeyer type modifications of the classical bernstein szasz and baskakov operators and deal with two different kind of problems firstly we obtain new results concerning preservation of shape properties lipschitz constants and global smoothness as well as monotonic convergence under convexity to do this we use a probabilistic approach based on representations of these operators in terms of stochastic processes having a s nondecreasing paths and satisfying a suitable martingale type condition secondly we show that the szasz durrmeyer operator is the limit in an appropriate sense of both the bernstein durrmeyer and the baskakov durrmeyer operators we provide rates of convergence which are derived from the bounds for the total variation distance between the probability measures involved

coupling discontinuous galerkin and mixed finite element discretizations using mortar finite elements discontinuous galerkin dg and mixed finite element mfe methods are two popular methods that possess local mass conservation in this paper we investigate dg dg and dg mfe domain decomposition couplings using mortar finite elements to impose weak continuity of fluxes and pressures on the interface the subdomain grids need not match and the mortar grid may be much coarser giving a two scale method convergence results in terms of the fine subdomain scale h and the coarse mortar scale h are established for both types of couplings in addition a nonoverlapping parallel domain decomposition algorithm is developed which reduces the coupled system to an interface mortar problem the properties of the interface operator are analyzed

space time domain decomposition methods for diffusion problems in mixed formulations this paper is concerned with global in time nonoverlapping domain decomposition methods for the mixed formulation of the diffusion problem two approaches are considered one uses the time dependent steklov poincare operator and the other uses optimized schwarz waveform relaxation oswr based on robin transmission conditions for each method a mixed formulation of an interface problem on the space time interfaces between subdomains is derived and different time grids are employed to adapt to different time scales in the subdomains demonstrations of the well posedness of the robin subdomain problems involved in the oswr method and a convergence proof of the oswr algorithm are given for the mixed formulation numerical results for two dimensional problems with strong heterogeneities are presented to illustrate the performance of the two methods

nonconforming finite element methods for the simulation of waves in viscoelastic solids the propagation of waves in two and three dimensional bounded viscoelastic media is described in the space frequency domain leading to a helmholtz type boundary value problem which is noncoercive non hermitian and complex valued first order absorbing boundary conditions are derived and used to minimize spurious reflections from the artificial boundaries the paper consists of two parts in part i we describe the global procedures for the approximate solution of the problem simplicial and rectangular nonconforming finite element methods are employed for the spatial discretization optimal error estimate in a broken energy and l2 norms are derived using a bootstrapping argument of schatz also a hybridization of these procedures is analyzed in part ii we define and analyze nonoverlapping domain decomposition iterative methods convergence results are derived and numerical experiments showing the potential applicability in seismology are presented

mixed finite element domain decomposition for nonlinear parabolic problems abstract fully discrete mixed finite element method is considered to approximate the solution of a nonlinear second order parabolic problem a massively parallel iterative procedure based on domain decomposition technique is presented to solve resulting nonlinear algebraic equations robin type boundary conditions are used to transmit information between subdomains the convergence of the iteration for each time step is demonstrated optimal order error estimates are also derived numerical examples are given

a smoothed em approach to indirect estimation problems with particular reference to stereology and emission tomography there are many practical problems where the observed data are not drawn directly from the density g of real interest but rather from another distribution derived from g by the application of an integral operator the estimation of g then entails both statistical and numerical difficulties a natural statistical approach is by maximum likelihood conveniently implemented using the em algorithm but this provides unsatisfactory reconstructions of g in this paper we modify the maximum likelihood em approach by introducing a simple smoothing step at each em iteration in our experience this algorithm converges in relatively few iterations to good estimates of g that do not depend on the choice of starting configuration some theoretical background is given that relates this smoothed em algorithm to a maximum penalized likelihood approach two applications are considered in detail the first is the classical stereology problem of determining particle size distributions from data collected on a plane section through a composite medium the second concerns the recovery of the structure of a section of the human body from external observations obtained by positron emission tomography for this problem we also suggest several technical improvements on existing methodology

analysis of finite element methods and domain decomposition algorithms for a fluid solid interaction problem this paper is concerned with the finite element galerkin approximations for a fluid solid interaction model proposed in x feng p lee and y wei appl anal submitted both continuous time and discrete time approximations are formulated and analyzed optimal order a priori estimates for the errors in l infty h 1 and l infty l 2 are derived the main difficulty for the error estimates is caused by the interface conditions which describe the interaction between a fluid and a solid on their contact surface and it is overcome by using a boundary duality argument of douglas and dupont numer math 20 1973 pp 213 237 to handle the terms involving the interface conditions parallelizable domain decomposition algorithms are also proposed and analyzed for efficiently solving the finite element systems

fitting a multiplicative incidence model to age and time specific prevalence data we discuss the assessment of age and time specific disease incidence using prevalence data a method is described for conveniently fitting a discrete time multiplicative model subject to positivity constraints using the em algorithm together with smoothing it allows essentially nonparametric assessment of incidence trends the method is illustrated using previously analyzed data on toxoplasmosis

recovery of ruin probability and value at risk from the scaled laplace transform inversion abstract in this paper we propose three modified approximations of the ruin probability and the inverse function of the ruin probability using the inversion of the scaled values of laplace transform suggested by mnatsakanov et al 2015 the problem of evaluating numerically the tail value at risk of an insurance portfolio is also discussed briefly performances of the proposed constructions are demonstrated via the graphs and tables using several examples

best constants for tensor products of bernstein type operators abstract for the tensor product of k copies of the same one dimensional bernstein type operator l we consider the problem of finding the best constant in preservation of the usual modulus of continuity for the l p norm on r k two main results are obtained the first one gives both necessary and sufficient conditions in order that 1 k 1 1 p is the best uniform constant for a single operator the second one gives sufficient conditions in order that 1 k 1 1 p is the best uniform constant for a family of operators the general results are applied to several classical families of operators usually considered in approximation theory throughout the paper probabilistic concepts and methods play an important role

a domain decomposition method for the helmholtz equation and related optimal control problems we present an iterative domain decomposition method to solve the helmholtz equation and related optimal control problems the proof of convergence of this method relies on energy techniques this method leads to efficient algorithms for the numerical resolution of harmonic wave propagation problems in homogeneous and heterogeneous media

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

least squares galerkin procedures for pseudohyperbolic equations abstract two least squares galerkin finite element schemes are formulated to solve pseudohyperbolic equations the advantage of this method is that it is not subject to the lbb condition the convergence analysis shows that the methods both yield the approximate solutions with optimal accuracy in l 2 2 l 2 moreover the two methods get the approximate solutions with first order and second order accuracy in time increment respectively numerical example shows that the two schemes are effective

artificial damping techniques for scalar waves in the frequency domain abstract an artificial damping algorithm for solving the helmholtz problem is considered when the imaginary part of the wave number is small the problem is known to be difficult to solve in this paper we propose an efficient artificial damping algorithm which can be viewed as a rational iteration each damped problem is solved incompletely by a nonoverlapping domain decomposition method convergence arguments are presented numerical results run on an ncube2 are presented to demonstrate the effectiveness of the method

on the approximation of convex functions by bernstein type operators abstract as a consequence of jensen s inequality centered operators of probabilistic type also called bernstein type operators approximate convex functions from above starting from this fact we consider several pairs of classical operators and determine in each case which one is better to approximate convex functions in almost all the discussed examples the conclusion follows from a simple argument concerning composition of operators however when comparing szasz mirakyan operators with bernstein operators over the positive semi axis the result is derived from the convex ordering of the involved probability distributions analogous results for non centered operators are also considered

modeling flow in porous media with double porosity permeability a stabilized mixed formulation error analysis and numerical solutions abstract the flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon dioxide sequestration the flow within numerous natural and synthetic porous materials that contain multiple scales of pores cannot be adequately described by the classical darcy equations it is for this reason that mathematical models for fluid flow in media with multiple scales of pores have been proposed in the literature however these models are analytically intractable for realistic problems in this paper a stabilized mixed four field finite element formulation is presented to study the flow of an incompressible fluid in porous media exhibiting double porosity permeability the stabilization terms and the stabilization parameters are derived in a mathematically consistent manner and the computationally convenient equal order interpolation of all the field variables is shown to be stable a systematic error analysis is performed on the resulting stabilized weak formulation representative problems patch tests and numerical convergence analyses are performed to illustrate the performance and convergence behavior of the proposed mixed formulation in the discrete setting the accuracy of numerical solutions is assessed using the mathematical properties satisfied by the solutions of this double porosity permeability model moreover it is shown that the proposed framework can perform well under transient conditions and that it can capture well known instabilities such as viscous fingering

unified primal formulation based a priori and a posteriori error analysis of mixed finite element methods we derive in this paper a unified framework for a priori and a posteriori error analysis of mixed finite element discretizations of second order elliptic problems it is based on the classical primal weak formulation the postprocessing of the potential proposed in t arbogast and z chen on the implementation of mixed methods as nonconforming methods for second order elliptic problems math comp 64 1995 943 972 and the discrete friedrichs inequality our analysis in particular avoids any explicit use of the uniform discrete inf sup condition and in a straightforward manner and under minimal necessary assumptions known convergence and superconvergence results are recovered the same framework then turns out to lead to optimal a posteriori energy error bounds in particular estimators for all families and orders of mixed finite element methods on grids consisting of simplices or rectangular parallelepipeds are derived they give a guaranteed and fully computable upper bound on the energy error represent error local lower bounds and are robust under some conditions on the diffusion dispersion tensor they are thus suitable for both overall error control and adaptive mesh refinement moreover the developed abstract framework and a posteriori error estimates are quite general and apply to any locally conservative method we finally prove that in parallel and simultaneously in converse to galerkin finite element methods under some circumstances the weak solution is the orthogonal projection of the postprocessed mixed finite element approximation onto the h 1 0 space and also establish several links between mixed finite element approximations and some generalized weak solutions

a parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods a parallelizable interative procedure based on domain decomposition techniques is defined and analyzed for mixed finite element methods for elliptic equations with the analysis being presented for the decomposition of the domain into the individual elements associated with the mixed method or into larger subdomains applications to time dependent problems are indicated

space time domain decomposition and mixed formulation for solving reduced fracture models in this paper we are interested in the fast path fracture and we aim to use global in time nonoverlapping domain decomposition methods to model flow and transport problems in a porous medium containing such a fracture we consider a reduced model in which the fracture is treated as an interface between the two subdomains two domain decomposition methods are considered one uses the time dependent steklovpoincare operator and the other uses optimized schwarz waveform relaxation oswr based on ventcell transmission conditions for each method a mixed formulation of an interface problem on the space time interface is derived and different time grids are employed to adapt to different time scales in the subdomains and in the fracture demonstrations of the well posedness of the ventcell subdomain problems is given for the mixed formulation an analysis for the convergence factor of the oswr algorithm is given in the case with fractures to compute the optimized parameters numerical results for two dimensional problems with strong heterogeneities are presented to illustrate the performance of the two methods