Volume 22, pp. 1-16, 2006.

Two-level additive Schwarz preconditioners for fourth-order mixed methods

M. R. Hanisch

Abstract

A two-level additive Schwarz preconditioning scheme for solving Ciarlet-Raviart, Hermann-Miyoshi, and Hellan-Hermann-Johnson mixed method equations for the biharmonic Dirichlet problem is presented. Using suitably defined mesh-dependent forms, a unified approach, with ties to the work of Brenner for nonconforming methods, is provided. In particular, optimal preconditioning of a Schur complement formulation for these equations is proved on polygonal domains without slits, provided the overlap between subdomains is sufficiently large.

Full Text (PDF) [253 KB]

Key words

additive Schwarz preconditioner, mixed finite elements, biharmonic equation, domain decomposition, mesh dependent norms

AMS subject classifications

65F10, 65N30, 65N55

< Back