Le Borne, SabineSabineLe BorneOvall, Jeffrey S.Jeffrey S.Ovall2020-02-182020-02-182012-05-08Numerical Linear Algebra with Applications 5 (20): 743-760 (2013)http://hdl.handle.net/11420/4951We 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.en1099-150620125743760Wileyblock gauss-seidelhierarchical baseshierarchical matriceshigher-order finite elementsMathematikJournal Article10.1002/nla.1841Other