Stability of ALE space-time discontinuous Galerkin method

Abstract

We assume the heat equation in a time dependent domain, where the evolution of the domain is given by the prescribed mapping. The problem is discretized by the discontinuous Galerkin method in space as well as in time with the aid of Arbitrary Lagrangian-Eulerian (ALE) method.

The sketch of the proof of the stability of the method is shown.

Keywords

• ALE formulation
• discontinuous Galerkin method
• discrete characteristic function
• stability