An iterative substructuring algorithm for a C\u3csup\u3e0\u3c/sup\u3e interior penalty method

We study an iterative substructuring algorithm for a C interior penalty method for the biharmonic problem. This algorithm is based on a Bramble-Pasciak-Schatz preconditioner. The condition number of the preconditioned Schur complement operator is shown to be bounded by C (1 + ln(H/h)) , where h is the mesh size of the triangulation, H represents the typical diameter of the nonoverlapping subdomains, and the positive constant C is independent of h, H, and the number of subdomains. Corroborating numerical results are also presented. Copyright © 2012, Kent State University. 0