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A Domain Decomposition Preconditioner for p-FEM Discretizations of Two-dimensional Elliptic Problems

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Abstract

In this paper, a uniformly elliptic second order boundary value problem in 2-D discretized by the p-version of the finite element method is considered. An inexact Dirichlet-Dirichlet domain decomposition pre-conditioner for the system of linear algebraic equations is investigated. Two solvers for the problem in the sub-domains, a pre-conditioner for the Schur-complement and an extension operator operating from the edges of the elements into the interior are proposed as ingredients for the inexact DD-pre-conditioner. In the main part of the paper, several numerical experiments on a parallel computer are given.

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  1. Institute for Computational Mathematics, Altenbergerstraße 69, 4040, Linz-Auhof, Austria

    S. Beuchler

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Beuchler, S. A Domain Decomposition Preconditioner for p-FEM Discretizations of Two-dimensional Elliptic Problems. Computing 74, 299–317 (2005). https://doi.org/10.1007/s00607-004-0091-1

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