Uniformly Convergent Iterative Methods for Discontinuous Galerkin Discretizations

Authors:
Blanca Ayuso De Dios;Ludmil Zikatanov
Affiliations:
Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, Spain 28049;Department of Mathematics, Penn State University, University Park, USA 16802
Venue:
Journal of Scientific Computing
Year:
2009

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Abstract

We present iterative and preconditioning techniques for the solution of the linear systems resulting from several discontinuous Galerkin (DG) Interior Penalty (IP) discretizations of elliptic problems. We analyze the convergence properties of these algorithms for both symmetric and non-symmetric IP schemes. The iterative methods are based on a "natural" decomposition of the first order DG finite element space as a direct sum of the Crouzeix-Raviart non-conforming finite element space and a subspace that contains functions discontinuous at interior faces. We also present numerical examples confirming the theoretical results.