A non-overlapping domain decomposition method for parabolic initial-boundary value problems Original Research Article

A non-overlapping domain decomposition method with adaptive interface conditions is applied to parabolic initial-boundary value problems in the full range from diffusion- to advection-dominated problems. The basic discretizations are the discontinuous Galerkin method in time and a stabilized Galerkin method in space. A convergence proof is available in appropriate Sobolev norms for the continuous elliptic problems arising in each time step. The numerical convergence rate is independent of the mesh size. Finally we extend the approach to more complex problems.