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

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 L²-norm for these procedures. This error estimate not only includes the optimal H¹-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.