New finite volume element methods in the ALE framework for time-dependent convection–diffusion problems in moving domains

Abstract

This paper develops new finite volume element methods (FVEMs) in the Arbitrary Lagrangian–Eulerian (ALE) framework for the time-dependent convection–diffusion problems on moving domains. In particular, we present two fully discrete schemes, one is based on the implicit Euler (IE) discretization and the other is based on the combination of the IE and geometric conservation laws (GCL). Stability and error estimation are analyzed for these two schemes. The second scheme satisfying the GCL demonstrates better on stability for long time simulations. Finally, numerical experiments are carried out to illustrate the theoretical results.