Analysis of a domain-splitting method for nonstationary convection- diffusion problems.

*(English)*Zbl 0836.65100Summary: We give an analysis of a method for the parallel solution of non- stationary convection-diffusion problems. The discretization is by the streamline diffusion finite element method combined with the blockwise implicit time stepping; the overlapping domain decomposition is used. The missing interior boundary values are predicted by extrapolation in time. This approach was first proposed and analyzed by H. Blum, S. Lisky and R. Rannacher [Computing 49, No. 1, 11-23 (1992; Zbl 0767.65073)] for strongly parabolic problems for which it has satisfactory stability and approximation properties. Here, we extend these results to convection-diffusion problems with dominant transport where the necessary numerical damping is introduced by streamline diffusion. The argument is entirely based on energy techniques and applies to general finite element discretizations.

##### MSC:

65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |

65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |

65M12 | Stability and convergence of numerical methods 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 |

65Y05 | Parallel numerical computation |

35K15 | Initial value problems for second-order parabolic equations |