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Uniformly Convergent Iterative Methods for Discontinuous Galerkin Discretizations

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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.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, 28049, Spain

    Blanca Ayuso de Dios

  2. Department of Mathematics, Penn State University, University Park, PA, 16802, USA

    Ludmil Zikatanov

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  1. Blanca Ayuso de Dios
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  2. Ludmil Zikatanov
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Correspondence to Ludmil Zikatanov.

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Ayuso de Dios, B., Zikatanov, L. Uniformly Convergent Iterative Methods for Discontinuous Galerkin Discretizations. J Sci Comput 40, 4–36 (2009). https://doi.org/10.1007/s10915-009-9293-1

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  • DOI: https://doi.org/10.1007/s10915-009-9293-1

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