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

## 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.

Item type: | Article |
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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 |

Related URLs: | |

Depositing user: | Strathprints Administrator |

Date Deposited: | 12 Nov 2007 |

Last modified: | 04 Sep 2014 17:45 |

URI: | http://strathprints.strath.ac.uk/id/eprint/4706 |

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