A non-overlapping domain decomposition method for parabolic initial-boundary value problems
Application of a non-overlapping domain decomposition method to a time dependent advection-reaction-diffusion model is the main goal of this paper. A discontinuous Galerkin method in time and a stabilized Galerkin method in space are the basic discretizations. For the continuous elliptic problems arising in each time step a convergence proof is available in appropriate Sobolev norms. The numerical convergence rate is independent of the mesh size. Several numerical examples in two space variables with exact solutions are included and the time dependent discrete relative \(L_2\) errors are presented. Finally the proposed approach can be extended for more complex (also nonlinear) problems as can be shown at the end of this paper.
non-overlapping domain decomposition method
parabolic initial boundary value problems
scientific article; zbMATH DE number 1311281