A posteriori error analysis for time-dependent Ginzburg-Landau type equations
type: Item
instance of: scholarly article
title: A posteriori error analysis for time-dependent Ginzburg-Landau type equations
zbMATH Open document ID: 1073.65089
author: Sören Bartels
published in: Numerische Mathematik
publication date: 2005-04-14T00:00:00Z
review text: Ginzburg-Landau type equations are considered in a bounded Lipschitz domain in two and three space dimensions. In is shown that an adaptive finite element method based on a posteriori error estimates allows automatic mesh and time step size refinement. An upper bound for the error is computed in each time step using a post processing procedure which consits in solving a self-adjoint eigenvalue problem. The dependance of the error estimate on the parameter epsilon is explicitely determined and can be used in to define local mesh refinement indicators. Three numerical examples for Allen-Cahn and Ginzburg-Landau equations in two spatial dimensions illustrate typical properties of the approach.
reviewed by: Kai Schneider
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35Q72
zbMATH DE Number: 2155987
zbMATH Keywords: eigenvalue problem
zbMATH Keywords: Allen-Cahn equation
zbMATH Keywords: Ginzburg-Landau type equations
zbMATH Keywords: adaptive finite element method
zbMATH Keywords: error estimates
zbMATH Keywords: mesh refinement
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: s00211-004-0560-7
OpenAlex ID: W2169845605
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DOI: 10.1007/S00211-004-0560-7
description: scientific article; zbMATH DE number 2155987