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

作者：Mackenzie J A^*; Mekwi W R

来源：IMA Journal of Numerical Analysis, 2012, 32(3): 888-905.

DOI：10.1093/imanum/drr021

• adaptivity
• moving meshes
• ALE-FEM schemes
• stability
• geometric conservation law

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 theta-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.

• 出版日期2012-7