Optimized Schwarz waveform relaxation and discontinuous Galerkin time stepping for heterogeneous problems. (English) Zbl 1262.65127
The paper deals with a numerical solution of a nonstationary linear convection-diffusion-reaction equation with strongly heterogeneous coefficients, particulary they are regular on several subdomains. The interfaces are curved in general, the Ventcell transmission conditions are employed. The authors propose and analyze a Schwarz waveform relaxation algorithm for a domain decomposition method. They deal with the semidiscretization in time and with the time discontinuous Galerkin method. Two-dimensional numerical examples, using generalized mortar finite elements in space, are presented.
Reviewer: Vit Dolejsi (Praha)
MSC:
| 65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
