## 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 $C \left(1+\ln(\tfrac{H}{h})\right)^2$, 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.

Full Text (PDF) [268 KB], BibTeX

### Key words

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

65N55, 65N30

### Links to the cited ETNA articles

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

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