Defect correction and domain decomposition for second-order boundary value problems

摘要

Highly accurate approximation is obtained through the techniques of defect correction and domain decomposition for second-order elliptic boundary value problems on a disc. The basic solution is computed using the Schwarz domain decomposition procedure and bilinear Galerkin finite element approximation on each subdomain to get an O(h2) accurate basic solution in higher-order discrete Sobolev norms. The defects are then computed using high-order polynomials (Lagrange polynomials or splines) to get as many O(h2) corrections as possible.