An analysis of stability and convergence of a finite-difference discretization of a model parabolic PDE in 1D using a moving mesh

J.A. MacKenzie, W. Mekwi

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

The aim of this paper is to investigate the stability and convergence of time integration schemes for the solution of a semi-discretization of a model parabolic problem in 1D using a moving mesh. The spatial discretization is achieved using a second-order central finite-difference scheme. Using energy techniques we show that the backward Euler scheme is unconditionally stable in a mesh-dependent L2-norm, independently of the mesh movement, but the Crank-Nicolson (CN) scheme is only conditionally stable. By identifying the diffusive and anti-diffusive effects caused by the mesh movement, we devise an adaptive {theta}-method that is shown to be unconditionally stable and asymptotically second-order accurate. Numerical experiments are presented to back up the findings of the analysis.
Original languageEnglish
Pages (from-to)507-528
Number of pages22
JournalIMA Journal of Numerical Analysis
Volume27
Issue number3
DOIs
Publication statusPublished - 2007

Keywords

  • adaptivity
  • moving meshes
  • ALE schemes
  • stability
  • numerical mathematics

Fingerprint Dive into the research topics of 'An analysis of stability and convergence of a finite-difference discretization of a model parabolic PDE in 1D using a moving mesh'. Together they form a unique fingerprint.

  • Cite this