Maximum norm a posteriori error estimation for parabolic problems using elliptic reconstructions

Natalia Kopteva, Torsten Linss

Research output: Contribution to journalArticle

10 Citations (Scopus)
43 Downloads (Pure)

Abstract

A semilinear second-order parabolic equation is considered in a regular and a singularly perturbed regime. For this equation, we give computable a posteriori error estimates in the maximum norm. Semidiscrete and fully discrete versions of the backward Euler, Crank--Nicolson, and discontinuous Galerkin $dG(r)$ methods are addressed. For their full discretizations, we employ elliptic reconstructions that are, respectively, piecewise-constant, piecewise-linear, and piecewise-quadratic for $r=1$ in time. We also use certain bounds for the Green's function of the parabolic operator.



Original languageEnglish
Pages (from-to)1494-1524
Number of pages31
JournalSIAM Journal on Numerical Analysis
Volume51
Issue number3
Early online date22 May 2013
DOIs
Publication statusPublished - 2013

Keywords

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

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