On the uniform stability of the space-time discontinuous Galerkin method for nonstationary problems in time-dependent domains
Abstract
In this paper we investigate the stability of the space-time discontinuous Galerkin method (STDGM) for the solution of nonstationary, linear convection-diusion-reaction problem in time-dependent domains formulated with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The stability is uniform with respect to the diusion coecient.
The ALE method replaces the classical partial time derivative with the so called ALE-derivative and an additional convective term. In the second part of the paper we discretize our problem using the space-time discontinuous Galerkin method.
In the formulation of the numerical scheme we use the nonsymmetric, symmetric and incomplete versions of the space discretization of diffusion terms and interior and boundary penalty. The space discretization uses piecewise polynomial approximations of degree p greater than 1, in time we use only piecewise linear discretization.
Finally in the third part of the paper we present our results concerning the uniform unconditional stability of the method.