A primal mixed domain decomposition procedure based on the nonconforming streamline diffusion method
This very important paper presents a new domain decomposition procedure for convection-diffusion problems. The nonconforming streamline diffusion method to resolve convection dominated problems, and Robin-type boundary conditions to transmit information between subdomains is used. The purpose of the author is to introduce a parallel iterative decomposition procedure with nonconforming primal mixed finite elements for convection dominated problems. Main result: The principal characteristic of the proposed algorithm is that the algorithm can be implemented very easily and naturally on a massively parallel mashine by assigning each subproblem to its own processor. Existence and uniqueness for the weak formulation of the convection-diffusion problem by a primal mixed method are precisely analyzed. Here the convergence of the parallel iterative procedure is shown. Finally, the author illustrates how theoretical results (the precise proofs of crucial assertion are proposed) can be used for the numerical realizations at given model examples.
scientific article; zbMATH DE number 2085833