Two-level additive Schwarz preconditioners for \(C^0\) interior penalty methods (Q2580999)

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