roe solver with entropy corrector for uncertain hyperbolic systems this paper deals with intrusive galerkin projection methods with a roe type solver for treating uncertain hyperbolic systems using a finite volume discretization in physical space and a piecewise continuous representation at the stochastic level the aim of this paper is to design a cost effective adaptation of the deterministic dubois and mehlman corrector to avoid entropy violating shocks in the presence of sonic points the adaptation relies on an estimate of the eigenvalues and eigenvectors of the galerkin jacobian matrix of the deterministic system of the stochastic modes of the solution and on a correspondence between these approximate eigenvalues and eigenvectors for the intermediate states considered at the interface we derive some indicators that can be used to decide where a correction is needed thereby reducing the computational costs considerably the effectiveness of the proposed corrector is assessed on the burgers and euler equations including sonic points

sharp l 2 error estimates and superconvergence of mixed finite element methods for non fickian flows in porous media a sharper l2 error estimate is obtained for the non fickian flow of fluid in porous media by means of a mixed ritz volterra projection instead of the mixed ritz projection used in r e ewing y lin and j wang acta math univ comenian n s 70 2001 pp 75 84 moreover local l2 superconvergence for the velocity along the gauss lines and for the pressure at the gauss points is derived for the mixed finite element method via the ritz volterra projection and global l2 superconvergence for the velocity and the pressure is also investigated by virtue of an interpolation postprocessing technique on the basis of the superconvergence estimates some useful a posteriori error estimators are presented for this mixed finite element method

pointwise localized error estimates for parabolic finite element equations we derive pointwise weighted error estimates for a semidiscrete finite element method applied to parabolic equations the results extend those obtained by a h schatz for stationary elliptic problems in particular they show that the error is more localized for higher order elements

multi element generalized polynomial chaos for arbitrary probability measures we develop a multi element generalized polynomial chaos me gpc method for arbitrary probability measures and apply it to solve ordinary and partial differential equations with stochastic inputs given a stochastic input with an arbitrary probability measure its random space is decomposed into smaller elements subsequently in each element a new random variable with respect to a conditional probability density function pdf is defined and a set of orthogonal polynomials in terms of this random variable is constructed numerically then the generalized polynomial chaos gpc method is implemented element by element numerical experiments show that the cost for the construction of orthogonal polynomials is negligible compared to the total time cost efficiency and convergence of me gpc are studied numerically by considering some commonly used random variables me gpc provides an efficient and flexible approach to solving differential equations with random inputs especially for problems related to long term integration large perturbation and stochastic discontinuities

new results for identifiability of nonlinear systems the parameter identifiability problem of deterministic non linear control systems is studied relations between nonlinear observability nonlinear functional expansions the uniqueness theorem of nonlinear realization theory and identifiability are investigated by using these relations necessary and sufficient conditions for identifiability are obtained for the first time these results provide insight into the identifiability problem for nonlinear systems

state isomorphism approach to global identifiability of nonlinear systems global deterministic identifiability of nonlinear systems is studied by constructing the family of local state isomorphisms that preserve the structure of the parametric system the method is simplified for homogeneous systems where such isomorphisms are shown to be linear thereby reducing the identifiability problem to solving a set of algebraic equations the known conditions for global identifiability in linear and bilinear systems are special cases of these results

modeling studies and efficient numerical methods for proton exchange membrane fuel cell abstract in this paper a three dimensional 3d nonisothermal multiphysics two phase steady state transport model and its efficient numerical methods are systematically studied for a full proton exchange membrane fuel cell pemfc in the sense of efficiency and accuracy the conservation equations of mass momentum species charge and energy are fully addressed in view of nonisothermality and multiphase characteristics in addition from an accurate numerical discretization s point of view we present some new formulations for species equations by investigating the interactions among the species in a framework of the combined finite element upwind finite volume method some efficient numerical methods are developed in terms of kirchhoff transformation for the sake of a fast and convergent numerical simulation the 3d simulations demonstrate that the convergent solutions can be attained within 80 nonlinear iterations in contrast to the oscillating and nonconvergent iterations conducted by commercial flow solvers or in house code with standard finite element volume methods numerical convergence tests are carried out to verify the efficiency and accuracy of our numerical algorithms and techniques

multi resolution analysis of wiener type uncertainty propagation schemes a multi resolution analysis mra is applied to an uncertainty propagation scheme based on a generalized polynomial chaos pc representation the mra relies on an orthogonal projection of uncertain data and solution variables onto a multi wavelet basis consisting of compact piecewise smooth polynomial functions the coefficients of the expansion are computed through a galerkin procedure the mra scheme is applied to the simulation of the lorenz system having a single random parameter the convergence of the solution with respect to the resolution level and expansion order is investigated in particular results are compared to two monte carlo sampling strategies demonstrating the superiority of the mra for more complex problems however the mra approach may require excessive cpu times adaptive methods are consequently developed in order to overcome this drawback two approaches are explored the first is based on adaptive refinement of the multi wavelet basis while the second is based on adaptive block partitioning of the space of random variables computational tests indicate that the latter approach is better suited for large problems leading to a more efficient flexible and parallelizable scheme

analysis of fully discrete fem for miscible displacement in porous media with bear scheidegger diffusion tensor fully discrete galerkin finite element methods are studied for the equations of miscible displacement in porous media with the commonly used bear scheidegger diffusion dispersion tensor begin aligned d mathbf u gamma d m i mathbf u bigg alpha t i alpha l alpha t frac mathbf u otimes mathbf u mathbf u 2 bigg end aligned previous works on optimal order l infty 0 t l 2 norm error estimate required the regularity assumption nabla x partial td mathbf u x t in l infty 0 t l infty omega while the bear scheidegger diffusion dispersion tensor is only lipschitz continuous even for a smooth velocity field mathbf u in terms of the maximal l p regularity of fully discrete finite element solutions of parabolic equations optimal error estimate in l p 0 t l q norm and almost optimal error estimate in l infty 0 t l q norm are established under the assumption of d mathbf u being lipschitz continuous with respect to mathbf u

intrusive galerkin methods with upwinding for uncertain nonlinear hyperbolic systems this paper deals with stochastic spectral methods for uncertainty propagation and quantification in nonlinear hyperbolic systems of conservation laws we consider problems with parametric uncertainty in initial conditions and model coefficients whose solutions exhibit discontinuities in the spatial as well as in the stochastic variables the stochastic spectral method relies on multi resolution schemes where the stochastic domain is discretized using tensor product stochastic elements supporting local polynomial bases a galerkin projection is used to derive a system of deterministic equations for the stochastic modes of the solution hyperbolicity of the resulting galerkin system is analyzed a finite volume scheme with a roe type solver is used for discretization of the spatial and time variables an original technique is introduced for the fast evaluation of approximate upwind matrices which is particularly well adapted to local polynomial bases efficiency and robustness of the overall method are assessed on the burgers and euler equations with shocks

on existence and uniqueness results for a coupled system modeling miscible displacement in porous media initial boundary value problems for a nonlinear differential system of two equations are considered in this paper this system of equations one of elliptic form for the pressure and the other of parabolic form for the concentration of one fluid governs the miscible displacement of one incompressible fluid by another in a porous medium under some reasonable assumptions on the data it is proved that the system possesses a weak solution and uniqueness is also established for the semiclassical solution of the system

analysis and computation of the elastic wave equation with random coefficients we consider the stochastic initial boundary value problem for the elastic wave equation with random coefficients and deterministic data we propose a stochastic collocation method for computing statistical moments of the solution or statistics of some given quantities of interest we study the convergence rate of the error in the stochastic collocation method in particular we show that the rate of convergence depends on the regularity of the solution or the quantity of interest in the stochastic space which is in turn related to the regularity of the deterministic data in the physical space and the type of the quantity of interest we demonstrate that a fast rate of convergence is possible in two cases for the elastic wave solutions with high regular data and for some high regular quantities of interest even in the presence of low regular data we perform numerical examples including a simplified earthquake which confirm the analysis and show that the collocation method is a valid alternative to the more traditional monte carlo sampling method for approximating quantities with high stochastic regularity

discrete maximal regularity and the finite element method for parabolic equations maximal regularity is a fundamental concept in the theory of partial differential equations in this paper we establish a fully discrete version of maximal regularity for parabolic equations on a polygonal or polyhedral domain varomega we derive various stability results in the discrete l p 0 t l q varomega norms for the finite element approximation with the mass lumping to the linear heat equation our method of analysis is an operator theoretical one using pure imaginary powers of operators and might be a discrete version of the result of dore and venni as an application optimal order error estimates in those norms are proved furthermore we study the finite element approximation for semilinear heat equations with locally lipschitz continuous nonlinear terms and offer a new method for deriving optimal order error estimates some interesting auxiliary results including discrete gagliardo nirenberg and sobolev inequalities are also presented

well posedness for semidiscrete fractional cauchy problems with finite delay abstract we address the study of well posedness on lebesgue spaces of sequences for the following fractional semidiscrete model with finite delay 0 1 u n t u n u n f n n n 0 1 r n 0 where t is a bounded linear operator defined on a banach space x typically a space of functions like l p 1 p and corresponds to the time discretization of the continuous riemann liouville fractional derivative by means of the poisson distribution we characterize the existence and uniqueness of solutions in vector valued lebesgue spaces of sequences of the model 0 1 in terms of boundedness of the operator valued symbol z 1 z 1 i z t 1 z 1 z 1 whenever 0 1 and x satisfies a geometrical condition for this purpose we use methods from operator valued fourier multipliers and resolvent operator families associated to the homogeneous problem we apply this result to show a practical and computational criterion in the context of hilbert spaces

discrete maximal parabolic regularity for galerkin finite element methods the main goal of the paper is to establish time semidiscrete and space time fully discrete maximal parabolic regularity for the time discontinuous galerkin solution of linear parabolic equations such estimates have many applications they are essential for example in establishing optimal a priori error estimates in non hilbertian norms without unnatural coupling of spatial mesh sizes with time steps

maximal regularity of fully discrete finite element solutions of parabolic equations we establish the maximal ell p regularity for fully discrete finite element solutions of parabolic equations with time dependent lipschitz continuous coefficients the analysis is based on a dis

model order reduction for parametrized nonlinear hyperbolic problems as an application to uncertainty quantification abstract in this work we present a model order reduction mor technique for hyperbolic conservation laws with applications in uncertainty quantification uq the problem consists of a parametrized time dependent hyperbolic system of equations where the parameters affect the initial conditions and the fluxes in a non linear way the procedure utilized to reduce the order is a combination of a greedy algorithm in the parameter space a proper orthogonal decomposition pod in time and empirical interpolation method eim to deal with non linearities drohmann 2012 we provide under some hypothesis an error bound for the reduced solution with respect to the high order one the algorithm shows small errors and savings of the computational time up to 90 in the uq simulations which are performed to validate the algorithm

stability analyticity and almost best approximation in maximum norm for parabolic finite element equations we consider semidiscrete solutions in quasi uniform finite element spaces of order o hr of the initial boundary value problem with neumann boundary conditions for a second order parabolic differential equation with time independent coefficients in a bounded domain in r n we show that the semigroup on l defined by the semidiscrete solution of the homogeneous equation is bounded and analytic uniformly in h we also show that the semidiscrete solution of the inhomogeneous equation is bounded in the space time l norm modulo a logarithmic factor for r 2 and we give a corresponding almost best approximation property

a stochastic collocation method for the second order wave equation with a discontinuous random speed in this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions the speed is piecewise smooth in the physical space and depends on a finite number of random variables the numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials gauss points in the probability space this approach leads to the solution of uncoupled deterministic problems as in the monte carlo method we consider both full and sparse tensor product spaces of orthogonal polynomials we provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points for full and sparse tensor product spaces and under some regularity assumptions on the data in particular we show that unlike in elliptic and parabolic problems the solution to hyperbolic problems is not in general analytic with respect to the random variables therefore the rate of convergence may only be algebraic an exponential fast rate of convergence is still possible for some quantities of interest and for the wave solution with particular types of data we present numerical examples which confirm the analysis and show that the collocation method is a valid alternative to the more traditional monte carlo method for this class of problems

identifiability of homogeneous systems using the state isomorphism approach new results are presented concerning the state isomorphism approach to global identifiability analysis of parameterized classes of nonlinear state space systems with specified initial states in particular we study the class of homogeneous systems for which under certain conditions the local state isomorphism for a pair of indistinguishable parameter vectors is shown to be homogeneous of degree one for homogeneous polynomial systems conditions are given under which the local state isomorphism becomes linear here the issue of whether or not the observability rank condition holds at the origin is shown to be of key importance the scope of the results which extend to the multivariable case is discussed and illustrated by a number of worked examples this demonstrates how the developed theory can be put to use to investigate the global identifiability properties of parameterized model classes

an efficient s ddm iterative approach for compressible contamination fluid flows in porous media in this paper we develop an efficient splitting domain decomposition method s ddm for compressible contamination fluid flows in porous media over multiple block divided sub domains by combining the non overlapping domain decomposition splitting linearization and extrapolation techniques the proposed s ddm iterative approach divides the large domain into multiple block sub domains in each time interval the s ddm scheme is applied to solve the water head equation in which an efficient local multilevel scheme is used for computing the values of water head on the interfaces of sub domains and the splitting implicit scheme is used for computing the interior values of water head in sub domains and the s ddm scheme is then proposed to solve the concentration equation by combining the upstream volume technique numerical experiments are performed and analyzed to illustrate the efficiency of the s ddm iterative approach for simulating compressible contamination fluid flows in porous media the developed method takes the excellent attractive advantages of both the non overlapping domain decomposition and the splitting technique and reduces computational complexities large memory requirements and long computational durations

solution of stochastic partial differential equations using galerkin finite element techniques this paper presents a framework for the construction of galerkin approximations of elliptic boundary value problems with stochastic input data a variational formulation is developed which allows among others numerical treatment by the finite element method a theory of a posteriori error estimation and corresponding adaptive approaches based on practical experience can be utilized the paper develops a foundation for treating stochastic partial differential equations pdes which can be further developed in many directions

a new error analysis of characteristics mixed fems for miscible displacement in porous media the method of characteristics type is especially effective for convection dominated diffusion problems due to the nature of characteristic temporal discretization the method allows one to use a large time step in many practical computations while all previous theoretical analyses always required certain restrictions on the time stepsize here we present a new analysis to establish unconditionally optimal error estimates for a modified method of characteristics with a mixed finite element approximation to the miscible displacement problem in mathbb r d d 2 3 for this purpose we introduce a new characteristic time discrete system we prove that the l 2 error bound the characteristic time discrete systemof the fully discrete method of characteristics to the time discrete system is tau independent and the numerical solution is bounded in w 1 infty norm unconditionally with the boundedness optimal error estimates are established in a traditional manner numerical results confirm our th

uncertainty quantification for systems of conservation laws uncertainty quantification through stochastic spectral methods has been recently applied to several kinds of non linear stochastic pdes in this paper we introduce a formalism based on kinetic theory to tackle uncertain hyperbolic systems of conservation laws with polynomial chaos pc methods the idea is to introduce a new variable the entropic variable in bijection with our vector of unknowns which we develop on the polynomial basis by performing a galerkin projection we obtain a deterministic system of conservation laws we state several properties of this deterministic system in the case of a general uncertain system of conservation laws we then apply the method to the case of the inviscid burgers equation with random initial conditions and we present some preliminary results for the euler system we systematically compare results from our new approach to results from the stochastic galerkin method in the vicinity of discontinuities the new method bounds the oscillations due to gibbs phenomenon to a certain range through the entropy of the system without the use of any adaptative random space discretizations it is found to be more precise than the stochastic galerkin method for smooth cases but above all for discontinuous cases

technical communique some remarks about an identifiability result of nonlinear systems the aim of this paper is to give an example that shows the bad use of corollary 2 vajda et al 1989 p 233 in various applications chappell et al 1990 chappell and godfrey 1992 in order to prove identifiability results in uncontrolled systems

uniform estimates for eulerian lagrangian methods for singularly perturbed time dependent problems we prove a priori optimal order error estimates in a weighted energy norm for several eulerian lagrangian methods for singularly perturbed time dependent convection diffusion equations with full regularity the estimates depend only on certain sobolev norms of the initial and right hand side data but not on varepsilon or any norm of the true solution and so hold uniformly with respect to varepsilon we use the interpolation of spaces and stability estimates to derive an varepsilon uniform estimate for problems with minimal or intermediate regularity where the convergence rates are proportional to certain besov norms of the initial and right hand side data

discrete maximal l p regularity for finite element operators let a h h 0 be a family of elliptic finite element operators let i 0 t and consider the problem u h t a hu h t f h t t in i u h 0 0 in this paper we show that for 1 0 is said to have discrete maximal l p regularity

adaptive stochastic galerkin fem abstract a framework for residual based a posteriori error estimation and adaptive mesh refinement and polynomial chaos expansion for general second order linear elliptic pdes with random coefficients is presented a parametric deterministic elliptic boundary value problem on an infinite dimensional parameter space is discretized by means of a galerkin projection onto finite generalized polynomial chaos gpc expansions and by discretizing each gpc coefficient by a fem in the physical domain an anisotropic residual based a posteriori error estimator is developed it contains bounds for both contributions to the overall error the error due to gpc discretization and the error due to finite element discretization of the gpc coefficients in the expansion the reliability of the residual estimator is established based on the explicit form of the residual estimator an adaptive refinement strategy is presented which allows to steer the polynomial degree adaptation and the dimension adaptation in the stochastic galerkin discretization and embedded in the gpc adaptation loop also the finite element mesh refinement of the gpc coefficients in the physical domain asynchronous mesh adaptation for different gpc coefficients is permitted subject to a minimal compatibility requirement on meshes used for different gpc coefficients details on the implementation with the open source software framework alea are presented it is generic and is based on available stiffness and mass matrices of a fem for the deterministic nonparametric nominal problem evaluated in the fenics environment preconditioning of the resulting matrix equation and iterative solution are discussed numerical experiments in two spatial dimensions for membrane and plane stress boundary value problems on polygons are presented they indicate substantial savings in total computational complexity due to fe mesh coarsening in high gpc coefficients

input estimation in nonlinear dynamical systems using differential algebra techniques the paper considers the problem of estimating the unknown input of a nonlinear dynamical system described by polynomial or rational differential equations from a finite set of noisy output samples without additional information this problem is ill posed since the unknown function may belong to an arbitrary infinite dimensional space we tackle this difficulty by designing a novel class of fast regularization algorithms that relies upon differential algebra techniques monte carlo studies are used to demonstrate the effectiveness of the new approach

finite difference methods for a nonlinear and strongly coupled heat and moisture transport system in textile materials in this paper we study heat and moisture transport through porous textile materials with phase change described by a degenerate nonlinear and strongly coupled parabolic system an uncoupled finite difference method with semi implicit euler scheme in time direction is proposed for the system we prove the existence and uniqueness of the solution of the finite difference system the optimal error estimates in both discrete l 2 and h 1 norms are obtained under the condition that the mesh sizes and h are smaller than a positive constant which depends solely upon physical parameters involved numerical results are presented to confirm our theoretical analysis and compared with experimental data

convergence analysis of a mixed finite volume scheme for an elliptic parabolic system modeling miscible fluid flows in porous media we study a finite volume discretization of a strongly coupled elliptic parabolic pde system describing miscible displacement in a porous medium we discretize each equation by a finite volume scheme which allows a wide variety of unstructured grids in any space dimension and gives strong enough convergence for handling the nonlinear coupling of the equations we prove the convergence of the scheme as the time and space steps go to 0 finally we provide numerical results to demonstrate the efficiency of the proposed numerical scheme

identifiability of affine linear parameter varying models abstract in this paper the identifiability of discrete time affine linear parameter varying alpv models is studied examples are presented to show that in general the identifiability of alpv model parameterizations does not guarantee the identifiability of the lti parameterizations composed of frozen lti models a new sufficient and necessary condition is then introduced in order to guarantee the structural identifiability for alpv parameterizations the identifiability of this class of parameterizations is related to the lack of state space isomorphisms between any two models corresponding to different parameter values in addition we present a sufficient and necessary condition for local structural identifiability and a sufficient condition for global structural identifiability which are both based on the rank of a user defined matrix these latter conditions allow systematic verification of identifiability numerical examples are finally presented to illustrate our results

regularity of the diffusion dispersion tensor and error analysis of galerkin fems for a porous medium flow we study galerkin finite element methods for an incompressible miscible flow in porous media with the commonly used bear scheidegger diffusion dispersion tensor d bf u phi d m i bf u alpha t i alpha l alpha t frac bf u otimes bf u bf u 2 the traditional approach to optimal l infty 0 t l 2 error estimates is based on an elliptic ritz projection which usually requires the regularity of nabla x partial td bf u x t in l p omega t however the bear scheidegger diffusion dispersion tensor may not satisfy the regularity condition even for a smooth velocity field bf u a new approach is presented in this paper in terms of a parabolic projection which only requires the lipschitz continuity of d bf u with the new approach we establish optimal l p error estimates and an almost optimal l infty error estimate

an optimal order error estimate to ellam schemes for transient advection diffusion equations on unstructured meshes the eulerian lagrangian localized adjoint method ellam provides a general characteristic procedure for solving transient advection diffusion equations with general boundary conditions in a mass conservative manner in this paper we prove an optimal order error estimate in the l 2 norm and a superconvergence estimate in the energy norm for the ellam scheme to d dimensional transient advection diffusion equations with general flux boundary conditions on unstructured meshes

a stable time discretizations preserve maximal parabolic regularity it is shown that for a parabolic problem with maximal l p regularity for 1 p infty the time discretization by a linear multistep method or runge kutta method has maximal ell p regularity uniformly in the stepsize if the method is a stable and satisfies minor additional conditions in particular the implicit euler method the crank nicolson method the second order backward difference formula bdf and the radau iia and gauss runge kutta methods of all orders preserve maximal regularity the proof uses weis characterization of maximal l p regularity in terms of r boundedness of the resolvent a discrete operator valued fourier multiplier theorem by blunck and generating function techniques that have been familiar in the stability analysis of time discretization methods since the work of dahlquist the a alpha stable higher order bdf methods have maximal ell p regularity under an r boundedness condition in a larger sector as an illustration of the use of maximal regularity

error estimates of splitting galerkin methods for heat and sweat transport in textile materials this paper is concerned with a single component model of heat and vapor sweat transport through three dimensional porous textile materials with phase change which is described by a nonlinear degenerate and strongly coupled parabolic system an uncoupled splitting galerkin method with semi implicit euler scheme in time direction is proposed for the system in this method a linearized scheme is applied for the approximation to darcy s velocity simultaneously in the mass and energy equations which leads to physical conservation of the method in the flow convection the existence and uniqueness of solution of the finite element system is proved and the optimal error estimate in an energy norm is obtained numerical results are presented to confirm our theoretical analysis and are compared with experimental data

maximum norm analysis of completely discrete finite element methods for parabolic problems we consider full discretizations of linear parabolic initial value problems in any space dimension finite elements are used for the discretization in space the resulting semidiscrete problem is integrated in time by means of a strongly a theta acceptable rational method stability estimates are derived and error bounds are established in the maximum norm for both smooth and rough initial data

applications of discrete maximal l p regularity for finite element operators in this paper we present applications of discrete maximal lp regularity for finite element operators more precisely we show error estimates of order h2 for linear and certain semilinear problems in various lp norms discrete maximal regularity allows us to prove error estimates in a very easy and efficient way moreover we also develop interpolation theory for fractional powers of finite element operators and extend the results on discrete maximal lp regularity formerly proved by the author

numerical approximation of poroelasticity with random coefficients using polynomial chaos and hybrid high order methods abstract in this work we consider the biot problem with uncertain poroelastic coefficients the uncertainty is modeled using a finite set of parameters with prescribed probability distribution we present the variational formulation of the stochastic partial differential system and establish its well posedness we then discuss the approximation of the parameter dependent problem by non intrusive techniques based on polynomial chaos decompositions we specifically focus on sparse spectral projection methods which essentially amount to performing an ensemble of deterministic model simulations to estimate the expansion coefficients the deterministic solver is based on a hybrid high order discretization supporting general polyhedral meshes and arbitrary approximation orders we numerically investigate the convergence of the probability error of the polynomial chaos approximation with respect to the level of the sparse grid finally we assess the propagation of the input uncertainty onto the solution considering an injection extraction problem

discrete maximal regularity of time stepping schemes for fractional evolution equations in this work we establish the maximal ell p regularity for several time stepping schemes for a fractional evolution model which involves a fractional derivative of order alpha in 0 2 alpha ne 1 in time these schemes include convolution quadratures generated by backward euler method and second order backward difference formula the l1 scheme explicit euler method and a fractional variant of the crank nicolson method the main tools for the analysis include operator valued fourier multiplier theorem due to weis math ann 319 735 758 2001 doi 10 1007 pl00004457 and its discrete analogue due to blunck stud math 146 157 176 2001 doi 10 4064 sm146 2 3 these results generalize the corresponding results for parabolic problems

maximum norm stability and maximal l p lp regularity of fems for parabolic equations with lipschitz continuous coefficients in this paper we study the semi discrete galerkin finite element method for parabolic equations with lipschitz continuous coefficients we prove the maximum norm stability of the semigroup generated by the corresponding elliptic finite element operator and prove the space time stability of the parabolic projection onto the finite element space in l infty q t l qt and l p 0 t l q omega lp 0 t lq 1

ritz volterra projections to finite element spaces and applications to integrodifferential and related equations the object of this paper is to investigate the convergence of finite element approximations to solutions of parabolic and hyperbolic integrodifferential equations and also of equations of sobolev and viscoelasticity type the concept of ritz volterra projection will be seen to unify much of the analysis for the different types of problems optimal order error estimates are obtained in l p for 2 leqq p infty and almost optimal order pointwise results given

limits of variance based sensitivity analysis for non identifiability testing in high dimensional dynamic models in systems biology a common approach to model biological processes is to use large systems of nonlinear differential equations the associated parameter estimation problem then requires a prior handling of the global identifiability question in a realistic experimental framework the lack of a method able to solve this issue has indirectly encouraged the use of global sensitivity analysis to select the subset of parameters to estimate nevertheless the links between these two global analyses are not yet fully explored the present work reveals new bridges between sensitivity analyses and global non identifiability through the use of functions derived from the sobol high dimensional representation of the model output we particularly specify limits of variance based sensitivity tools to completely conclude on global non identifiability of parameters in a given experimental context

an optimal order error estimate for a family of ellam mfem approximations to porous medium flow mathematical models used to describe porous medium flow lead to coupled systems of time dependent nonlinear partial differential equations which present serious mathematical and numerical difficulties standard methods tend to generate numerical solutions with nonphysical oscillations or numerical dispersion along with spurious grid orientation effect the ellam mfem time stepping procedure in which an eulerian lagrangian localized adjoint method ellam is used to solve the transport equation and a mixed finite element method mfem is used for the pressure equation simulates porous medium flow accurately even if large spatial grids and time steps are used in this paper we prove an optimal order error estimate for a family of ellam mfem approximations

symmetric and nonsymmetric discontinuous galerkin methods for reactive transport in porous media for solving reactive transport problems in porous media we analyze three primal discontinuous galerkin dg methods with penalty namely symmetric interior penalty galerkin sipg nonsymmetric interior penalty galerkin nipg and incomplete interior penalty galerkin iipg a cut off operator is introduced in dg to treat general kinetic chemistry error estimates in l2 h1 are established which are optimal in h and nearly optimal in p we develop a parabolic lift technique for sipg which leads to h optimal and nearly p optimal error estimates in the l2 l2 and negative norms numerical results validate these estimates we also discuss implementation issues including penalty parameters and the choice of physical versus reference polynomial spaces

mathematical theory of stationary miscible filtration abstract we consider a coupled system of two elliptic partial differential equations that models stationary incompressible two component miscible displacement in porous media we suppose that the dispersion tensor depends on the velocity the so called peaceman model see e g d w peaceman soc pet eng j 6 1966 213 216 assuming that the mobility ratio is not too large we prove the existence of at least one solution in w r 2 w r 2 furthermore supposing that the data are small we also establish well posedness in w r 2 w l 1

an optimal order l2 error estimate for nonsymmetric discontinuous galerkin methods for a parabolic equation in multiple space dimensions we analyze the nonsymmetric discontinuous galerkin methods nipg and iipg for linear elliptic and parabolic equations with a spatially varied coefficient in multiple spatial dimensions we consider d linear approximation spaces on a uniform rectangular mesh but our results can be extended to smoothly varying rectangular meshes using a blending or boolean interpolation we obtain a superconvergence error estimate in a discrete energy norm and an optimal order error estimate in a semi discrete norm for the parabolic equation the l 2 optimality for the elliptic problem follows directly from the parabolic estimates numerical results are provided to validate our theoretical estimates we also discuss the impact of penalty parameters on convergence behaviors of nipg

global existence of weak solution to the heat and moisture transport system in fibrous porous media abstract this paper is concerned with theoretical analysis of a heat and moisture transfer model arising from textile industries which is described by a degenerate and strongly coupled parabolic system we prove the global in time existence of weak solution by constructing an approximate solution with some standard smoothing the proof is based on the physical nature of gas convection in which the heat energy flux in convection is determined by the mass vapor flux in convection

an approximation to miscible fluid flows in porous media with point sources and sinks by an eulerian lagrangian localized adjoint method and mixed finite element methods we develop an eulerian lagrangian localized adjoint method ellam mixed finite element method mfem solution technique for accurate numerical simulation of coupled systems of partial differential equations pdes which describe complex fluid flow processes in porous media an ellam which was shown previously to outperform many widely used methods in the context of linear convection diffusion pdes is presented to solve the transport equation for concentration since accurate fluid velocities are crucial in numerical simulations an mfem is used to solve the pressure equation for the pressure and darcy velocity this minimizes the numerical difficulties occurring in standard methods for approximating velocities caused by differentiation of the pressure and then multiplication by rough coefficients the ellam mfem solution technique significantly reduces temporal errors symmetrizes the governing transport equation eliminates nonphysical oscillation and or excessive numerical dispersion in many simulators conserves mass and treats boundary conditions accurately numerical experiments show that the ellam mfem solution technique simulates miscible displacements of incompressible fluid flows in porous media accurately with fairly coarse spatial grids and very large time steps which are one or two orders of magnitude larger than the time steps used in many methods moreover the ellam mfem solution technique can treat large mobility ratios discontinuous permeabilities and porosities anisotropic dispersion in tensor form and point sources and sinks