Two-level additive Schwarz preconditioners for C0 interior penalty methods

Abstract

We study two-level additive Schwarz preconditioners that can be used in the iterative solution of the discrete problems resulting from C0 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+(H3/δ3)), 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.