Discrete Maximal Lp Regularity for Finite Element Operators

DOI10.1137/040616553zbMath1118.65104OpenAlexW2081714730MaRDI QIDQ5470976

Matthias Geissert

Publication date: 2 June 2006

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/040616553

zbMATH Keywords

parabolic equationGalerkin finite element methodmaximal regularity

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Linear differential equations in abstract spaces (34G10)

Related Items (19)

Maximum-norm stability of the finite element Ritz projection under mixed boundary conditions ⋮ Maximum-norm stability of the finite element method for the Neumann problem in nonconvex polygons with locally refined mesh ⋮ A-Stable Time Discretizations Preserve Maximal Parabolic Regularity ⋮ Discrete maximal regularity of time-stepping schemes for fractional evolution equations ⋮ Maximal $L^p$ analysis of finite element solutions for parabolic equations with nonsmooth coefficients in convex polyhedra ⋮ Maximal Regularity of Fully Discrete Finite Element Solutions of Parabolic Equations ⋮ Large time step maximum norm regularity of L-stable difference methods for parabolic equations ⋮ Applications of discrete maximal \(L_p\) regularity for finite element operators ⋮ Analysis of fully discrete FEM for miscible displacement in porous media with Bear-Scheidegger diffusion tensor ⋮ Maximum-norm stability and maximal \(L^p\) regularity of FEMs for parabolic equations with Lipschitz continuous coefficients ⋮ Discrete maximal regularity and the finite element method for parabolic equations ⋮ Discrete maximal parabolic regularity for Galerkin finite element methods ⋮ Analyticity, maximal regularity and maximum-norm stability of semi-discrete finite element solutions of parabolic equations in nonconvex polyhedra ⋮ Runge-Kutta time discretization of nonlinear parabolic equations studied via discrete maximal parabolic regularity ⋮ Error analysis of a fully discrete finite element method for variable density incompressible flows in two dimensions ⋮ Stability, analyticity, and maximal regularity for parabolic finite element problems on smooth domains ⋮ Pointwise error estimates of linear finite element method for Neumann boundary value problems in a smooth domain ⋮ Discrete maximal regularity for abstract Cauchy problems ⋮ Regularity of the Diffusion-Dispersion Tensor and Error Analysis of Galerkin FEMs for a Porous Medium Flow

This page was built for publication: Discrete Maximal Lp Regularity for Finite Element Operators