Numerical study of maximum norm a posteriori error estimates for singularly perturbed parabolic problems

Natalia Kopteva, Torsten Linß

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A second-order singularly perturbed parabolic equation in one space dimension is considered. For this equation, we give computable a posteriori error estimates in the maximum norm for two semidiscretisations in time and a full discretisation using P1 FEM in space. Both the Backward-Euler method and the Crank-Nicolson method are considered. Certain critical details of the implementation are addressed. Based on numerical results we discuss various aspects of the error estimators in particular their effectiveness.

Original languageEnglish
Title of host publicationNumerical Analysis and Its Applications - 5th International Conference, NAA 2012, Revised Selected Papers
Pages50-61
Number of pages12
DOIs
Publication statusPublished - 2013
Event5th International Conference on Numerical Analysis and Applications, NAA 2012 - Lozenetz, Bulgaria
Duration: 15 Jun 201320 Jun 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8236 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th International Conference on Numerical Analysis and Applications, NAA 2012
Country/TerritoryBulgaria
CityLozenetz
Period15/06/1320/06/13

Keywords

  • a posteriori error estimate
  • backward Euler
  • Crank-Nicolson
  • elliptic reconstruction
  • maximum norm
  • parabolic equation
  • reaction-diffusion
  • singular perturbation

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