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

John Mackenzie, Wankere Mekwi

Research output: Contribution to journalArticlepeer-review

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 θ-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
Article number3
Pages (from-to)507-528
Number of pages22
JournalIMA Journal of Numerical Analysis
Volume27
Issue number3
DOIs
Publication statusPublished - Jul 2007
Externally publishedYes

Keywords

  • adaptivity
  • moving meshes
  • ALE schemes
  • stability

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