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IMA Journal of Numerical Analysis Advance Access originally published online on March 16, 2007
IMA Journal of Numerical Analysis 2008 28(1):1-24; doi:10.1093/imanum/drl046
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Additive Schwarz preconditioning for p-version triangular and tetrahedral finite elements

Joachim Schöberl{dagger}

Department for Mathematics, Center for Computational Engineering Science (CCES), Rheinisch-Westfälische Technische Hochschule (RWTH), Aachen, Germany

Jens M. Melenk{ddagger}

Institute for Analysis and Scientific Computing, University of Technology, Vienna, Austria

Clemens Pechstein§

Institute of Computational Mathematics, Johannes Kepler University, Linz, Austria

Sabine Zaglmayr

Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Science, Linz, Austria

{dagger} Email: schoeberl{at}mathcces.rwth-aachen.de

{ddagger} Email: melenk{at}tuwien.ac.at

§ Email: clemens.pechstein{at}numa.uni-linz.ac.at

Email: sabine.zaglmayr{at}oeaw.ac.at

Received on 13 May 2005. Revised on 6 December 2006.


  Abstract

This paper analyses two-level Schwarz methods for matrices arising from the p-version finite-element method on triangular and tetrahedral meshes. The coarse level consists of the lowest-order finite-element space. On the fine level, we investigate several decompositions with large or small overlap leading to optimal or close to optimal condition numbers. The analysis is confirmed by numerical experiments for a simple model problem and an elasticity problem on a complex geometry.

Key Words: high-order finite-element method; preconditioning


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