A posteriori error estimates by recovered gradients in parabolic finite element equations

DOI10.1007/s10543-008-0169-9zbMath1157.65055OpenAlexW2063306976MaRDI QIDQ960036

Dmitriy Leykekhman, Lars B. Wahlbin

Publication date: 16 December 2008

Published in: BIT (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1911/102056

zbMATH Keywords

numerical examplesfinite elementmethod of linesinitial boundary value problemsa posteriori error estimatestime discretizationsecond order parabolic equation

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

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Flexible patch post-processing recovery strategies for solution enhancement and adaptive mesh refinement ⋮ Global and Interior Pointwise best Approximation Results for the Gradient of Galerkin Solutions for Parabolic Problems ⋮ Optimal superconvergence and asymptotically exact \textit{a posteriori} error estimator for the local discontinuous Galerkin method for linear elliptic problems on Cartesian grids ⋮ Local and pointwise error estimates of the local discontinuous Galerkin method applied to the Stokes problem ⋮ Sharply local pointwise a posteriori error estimates for parabolic problems ⋮ An a posteriori error estimator for an unsteady advection-diffusion-reaction problem ⋮ Pointwise Best Approximation Results for Galerkin Finite Element Solutions of Parabolic Problems ⋮ Residual estimates for post-processors in elliptic problems

Cites Work

• Unnamed Item
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• Nonsmooth data error estimates for damped single step methods for parabolic equations in Banach space
• Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part 1: A smooth problem and globally quasi-uniform meshes
• Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems
• Superconvergence of the Gradient in Piecewise Linear Finite-Element Approximation to a Parabolic Problem
• Single step methods for inhomogeneous linear differential equations in Banach space
• Stability, analyticity, and almost best approximation in maximum norm for parabolic finite element equations
• Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates
• Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence
• Asymptotically Exact A Posteriori Error Estimators, Part II: General Unstructured Grids
• Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part II: The piecewise linear case