Preprint des Projektes: Sonstiges

01/08 Alexander Weddemann, Vera Thümmler.
Stability Analysis of ALE-Methods for Advection-Diffusion Problems

ALE-methods are frequently used to solve systems of partial differential equations (PDEs) on moving domains. The main idea of these methods is to incorporate the time evolution of the domain into the equations. However, the motion of the domain with respect to time induces convective fluxes in the resulting equations. These can lead to stability problems of the numerical method if they become too large. In this paper we show that these difficulties occur already in very simple systems. We discuss the stability properties of the implicit Euler method applied to a linear advection-diffusion problem on a moving domain and propose several ways of dealing with the stability problems. Furthermore, we compare the direct implementation of the ALE-equations via a weak formulation with the predefined ALE-mode of COMSOL Multiphysics.