Rapid error reduction for block Gauss–Seidel based on p-hierarchical basis


Correspondence to: J. S. Ovall, Department of Mathematics, University of Kentucky, 761 Patterson Office Tower, Lexington, KY 40506-0027, U.S.A.

E-mail: jovall@ms.uky.edu


We consider a two-level block Gauss–Seidel iteration for solving systems arising from finite element discretizations employing higher-order elements. A p-hierarchical basis is used to induce this block structure. Using superconvergence results normally employed in the analysis of gradient recovery schemes, we argue that a massive reduction of the H1-error occurs in the first iterate, so that the discrete solution is adequately resolved in very few iterates—sometimes a single iteration is sufficient. Numerical experiments on uniform and adapted meshes support these claims. Copyright © 2012 John Wiley & Sons, Ltd.