A posteriori error estimates by recovered gradients in parabolic finite element equations
type: Item
instance of: scholarly article
title: A posteriori error estimates by recovered gradients in parabolic finite element equations
zbMATH Open document ID: 1157.65055
published in: BIT
publication date: 2008-12-16T00:00:00Z
full work available at URL: http://hdl.handle.net/1911/102056
review text: The method of lines is often used to solve initial boundary value problems. Using this method, the problem is first discretized in space and the resulting system of ordinary differential equations is then approximated in time.The authors show that if the time discretization error is sufficienly small, compared to space discretization error then the elliptic averaging techniques work as well for parabolic problems [cf. \textit{S. Ziukas} and \textit{N.-E. Wiberg}, Lect. Notes Pure Appl. Math. 196, 303--314 (1998; Zbl 0903.65078)]. Numerical illustrations in support of the theoretical results are also given.
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 65M20
zbMATH DE Number: 5382747
zbMATH Keywords: a posteriori error estimates
zbMATH Keywords: finite element
zbMATH Keywords: second order parabolic equation
zbMATH Keywords: numerical examples
zbMATH Keywords: method of lines
zbMATH Keywords: initial boundary value problems
zbMATH Keywords: time discretization
author: Dmitriy Leykekhman
author: L. B. Wahlbin
MaRDI profile type: Publication
OpenAlex ID: W2063306976
cites work: Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence
cites work: Asymptotically Exact A Posteriori Error Estimators, Part II: General Unstructured Grids
cites work: Single step methods for inhomogeneous linear differential equations in Banach space
cites work: Nonsmooth data error estimates for damped single step methods for parabolic equations in Banach space
cites work: Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. I: A smooth problem and globally quasi-uniform meshes
cites work: Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems
cites work: Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates
cites work: Stability, analyticity, and almost best approximation in maximum norm for parabolic finite element equations
cites work: Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part II: The piecewise linear case
cites work: Q4360234
cites work: Superconvergence of the Gradient in Piecewise Linear Finite-Element Approximation to a Parabolic Problem
cites work: Q4394881
DOI: 10.1007/S10543-008-0169-9
description: scientific article; zbMATH DE number 5382747