A domain decomposition discretization of parabolic problems

Abstract. In recent years, domain decomposition methods have attracted much attention due to their successful application to many elliptic and parabolic problems. Domain decomposition methods treat problems based on a domain substructuring, which is attractive for parallel computation, due to the independence among the subdomains. In principle, domain decomposition methods may be applied to the system resulting from a standard discretization of the parabolic problems or, directly, be carried out through a direct discretization of parabolic problems. In this paper, a direct domain decomposition method is introduced to discretize the parabolic problems. The stability and convergence of this algorithm are analyzed, and an O(τ + h) error bound is provided.