Adaptive Crank-Nicolson methods with dynamic finite-element spaces for parabolic problems

Dongho Kim, Eun Jae Park

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We construct a posteriori error estimators for approximate solutions of linear parabolic equations. We consider discretizations of the problem by modified discontinuous Galerkin schemes in time and continuous Galerkin methods in space. Especially, finite element spaces are permitted to change at different time levels. Exploiting Crank-Nicolson reconstruction idea introduced by Akrivis, Makridakis & Nochetto [2], we derive space-time a posteriori error estimators of second order in time for the Crank-Nicolson-Galerkin finite element method.

Original languageEnglish
Pages (from-to)873-886
Number of pages14
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume10
Issue number4
DOIs
Publication statusPublished - 2008 Nov

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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