Two-level additive Schwarz preconditioners for C\u3csup\u3e0\u3c/sup\u3e interior penalty methods

We study two-level additive Schwarz preconditioners that can be used in the iterative solution of the discrete problems resulting from C interior penalty methods for fourth order elliptic boundary value problems. We show that the condition number of the preconditioned system is bounded by C(1+(H /δ )), where H is the typical diameter of a subdomain, δ measures the overlap among the subdomains and the positive constant C is independent of the mesh sizes and the number of subdomains. 0 3