Mackenzie, John and Mekwi, W.R. (2012) *An unconditionally stable second-order accurate ALE–FEM scheme for two-dimensional convection–diffusion problems.* IMA Journal of Numerical Analysis, 32 (3). pp. 888-905. ISSN 0272-4979

## Abstract

The aim of this paper is to investigate the stability of time integration schemes for the solution of a finite element semi-discretization of a scalar convection–diffusion equation defined on a moving domain. An arbitrary Lagrangian–Eulerian formulation is used to reformulate the governing equation with respect to a moving reference frame. We devise an adaptive θ-method time integrator that is shown to be unconditionally stable and asymptotically second-order accurate for smoothly evolving meshes. An essential feature of the method is that it satisfies a discrete equivalent of the well-known geometric conservation law. Numerical experiments are presented to confirm the findings of the analysis.

Item type: | Article |
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ID code: | 41131 |

Keywords: | adaptivity, moving meshes, ALE-FEMschemes, stability geometric conservation law, Probabilities. Mathematical statistics |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Pure Administrator |

Date Deposited: | 13 Sep 2012 16:24 |

Last modified: | 19 Sep 2012 12:13 |

URI: | http://strathprints.strath.ac.uk/id/eprint/41131 |

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