A Class of Domain Decomposition Preconditioners for hp-Discontinuous Galerkin Finite Element Methods

Authors:
Paola F. Antonietti;Paul Houston
Affiliations:
MOX---Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy 20133;School of Mathematical Sciences, University of Nottingham, Nottingham, UK NG7 2RD
Venue:
Journal of Scientific Computing
Year:
2011

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Abstract

In this article we address the question of efficiently solving the algebraic linear system of equations arising from the discretization of a symmetric, elliptic boundary value problem using hp-version discontinuous Galerkin finite element methods. In particular, we introduce a class of domain decomposition preconditioners based on the Schwarz framework, and prove bounds on the condition number of the resulting iteration operators. Numerical results confirming the theoretical estimates are also presented.