An unconditionally stable second-order accurate ALE–FEM scheme for two-dimensional convection–diffusion problems

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

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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.

Creators(s): Mackenzie, John ORCID logoORCID: https://orcid.org/0000-0003-4412-7057 and Mekwi, W.R.;
Item type:Article
ID code:41131
Keywords:adaptivity, moving meshes, ALE-FEMschemes, stability geometric conservation law, Probabilities. Mathematical statistics, Computational Mathematics, Applied Mathematics, Mathematics(all)
Subjects:Science > Mathematics > Probabilities. Mathematical statistics
Department:Faculty of Science > Mathematics and Statistics
Depositing user: Pure Administrator
Date deposited:13 Sep 2012 15:24
Last modified:20 Jan 2021 19:22
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URI:https://strathprints.strath.ac.uk/id/eprint/41131
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