Domain Splitting Algorithm for Mixed Finite

| In this paper we fromulate and study a domain decomposition algorithm for solving mixed nite element approximations to parabolic initial-boundary value problems. In contrast to the usual overlapping domain decomposition method this technique leads to noniterative algorithms, i.e. the subdomain problems are solved independently and the solution in the whole domain is obtained from the local solutions by restriction and simple averaging. The algorithm exploits the fact that the time discretization leads to an elliptic problem with a large positive coeecient in front of the zero order term. The solutions of such problems exhibit a boundary layer with thickness proportional to the square root of the time discretization parameter. Thus, any error in the boundary conditions will decay exponentially and a reasonable overlap will produce a suuciently accurate method. We prove that the proposed algorithm is stable in L 2-norm and has the same accuracy as the implicit method.