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

MacKenzie, J.A. and Mekwi, W. (2007) An analysis of stability and convergence of a finite-difference discretization of a model parabolic PDE in 1D using a moving mesh. IMA Journal of Numerical Analysis, 27 (3). pp. 507-528. ISSN 0272-4979

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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.

Creators(s): MacKenzie, J.A. ORCID logoORCID: https://orcid.org/0000-0003-4412-7057 and Mekwi, W.;
Item type:Article
ID code:4706
Keywords:adaptivity, moving meshes, ALE schemes, stability, numerical mathematics, Mathematics, Computational Mathematics, Applied Mathematics, Mathematics(all)
Subjects:Science > Mathematics
Department:Faculty of Science > Mathematics and Statistics
Faculty of Science > Mathematics and Statistics > Mathematics
Depositing user: Strathprints Administrator
Date deposited:12 Nov 2007
Last modified:20 Jan 2021 17:33
URI:https://strathprints.strath.ac.uk/id/eprint/4706
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