Uniformly convergent iterative methods for discontinuous Galerkin discretizations

Blanca Ayuso De Dios, Ludmil Tomov Zikatanov

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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.

Original languageEnglish (US)
Pages (from-to)4-36
Number of pages33
JournalJournal of Scientific Computing
Volume40
Issue number1-3
DOIs
Publication statusPublished - Jul 1 2009

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All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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