Parallel Galerkin domain decomposition procedures based on the streamline diffusion method for convection–diffusion problems

Abstract

Based upon the streamline diffusion method, parallel Galerkin domain decomposition procedures for convection–diffusion problems are given. These procedures use implicit method in the sub-domains and simple explicit flux calculations on the inter-boundaries of sub-domains by integral mean method or extrapolation method to predict the inner-boundary conditions. Thus, the parallelism can be achieved by these procedures. The explicit nature of the flux calculations induces a time step limitation that is necessary to preserve stability. Artificial diffusion parameters δ are given. By analysis, optimal order error estimate is derived in a norm which is stronger than L 2 -norm for these procedures. This error estimate not only includes the optimal H 1 -norm error estimate, but also includes the error estimate along the streamline direction ‖ β ⋅ ∇ ( u − U ) ‖ , which cannot be achieved by standard finite element method. Experimental results are presented to confirm theoretical results.