Space-Time Adaptive Methods for the Mixed Formulation of a Linear Parabolic Problem

Dongho Kim, Eun Jae Park, Boyoon Seo

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we are concerned with space-time a posteriori error estimators for fully discrete solutions of linear parabolic problems. The mixed formulation with Raviart–Thomas finite element spaces is considered. A new second-order method in time is proposed so that mixed finite element spaces are permitted to change at different time levels. The new method can be viewed as a variant Crank–Nicolson (CN) scheme. Introducing a CN reconstruction appropriate for the mixed setting, we construct an a posteriori error estimator of second order in time for the variant CN mixed scheme. Various numerical examples are given to test our space-time adaptive algorithm and validate the theory proved in the paper. In addition, numerical results for backward Euler and CN schemes are presented to compare their performance in the time adaptivity setting over uniform/adaptive spatial meshes.

Original languageEnglish
Pages (from-to)1725-1756
Number of pages32
JournalJournal of Scientific Computing
Volume74
Issue number3
DOIs
Publication statusPublished - 2018 Mar 1

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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