Volume 39, pp. 313-332, 2012.

An Iterative Substructuring Algorithm for a $C^0$ Interior Penalty Method

Susanne C. Brenner and Kening Wang

Abstract

We study an iterative substructuring algorithm for a $C^0$ 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 $C{(1+\ln (\frac{H}{h}))}^2$, 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.

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Key words

biharmonic problem, iterative substructuring, domain decomposition, $C^0$ interior penalty methods, discontinuous Galerkin methods

AMS subject classifications

65N55, 65N30

ETNA articles which cite this article

Vol. 49 (2018), pp. 81-102 D. Cho, L. F. Pavarino, and S. Scacchi: Isogeometric Schwarz preconditioners for the biharmonic problem