Coercive domain decomposition algorithms for advection-diffusion equations and systems

Abstract

Two families of non-overlapping coercive domain decomposition methods are proposed for the numerical approximation of advection dominated advection-diffusion equations and systems. Convergence is proven for both the continuous and the discrete problem. The rate of convergence of the first method is shown to be independent of the number of degrees of freedom. Several numerical results are presented, showing the efficiency and robustness of the proposed iterative algorithms.