A MULTILEVEL PRECONDITIONER FOR THE INTERIOR PENALTY DISCONTINUOUS GALERKIN METHOD

In this article we present a multilevel preconditioner for interior penalty discontinuous Galerkin discretizations of second order elliptic boundary value problems that gives rise to uniformly bounded condition numbers without any additional regularity assumptions on the solution. The underlying tri...

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Bibliographic Details
Published in:	SIAM journal on numerical analysis Vol. 46; no. 5; pp. 2742 - 2768
Main Authors:	BRIX, KOLJA, PINTO, MARTIN CAMPOS, DAHMEN, WOLFGANG
Format:	Journal Article
Language:	English
Published:	Philadelphia Society for Industrial and Applied Mathematics 01-01-2008
Subjects:	Children Conformity Galerkin methods Mathematical discontinuity Mathematics Numerical Analysis Polynomials Preconditioning Triangles Triangulation Vertices admissible averaging operators frames energy-stable splittings multilevel Schwarz preconditioners interior penalty method discontinuous Galerkin methods
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Summary:	In this article we present a multilevel preconditioner for interior penalty discontinuous Galerkin discretizations of second order elliptic boundary value problems that gives rise to uniformly bounded condition numbers without any additional regularity assumptions on the solution. The underlying triangulations are assumed only to be shape regular but may have hanging nodes subject to certain mild grading conditions. A key role is played by certain decompositions of the discontinuous trial space into a conforming subspace and a nonconforming subspace that is controlled by the jumps across the edges.
ISSN:	0036-1429 1095-7170
DOI:	10.1137/07069691X