Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations

Veselin A. Dobrev, Raytcho D. Lazarov, Panayot S. Vassilevski, Ludmil T. Zikatanov

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Abstract

This paper reviews some known and proposes some new preconditioning methods for a number of discontinuous Galerkin (or DG) finite element approximations for elliptic problems of second order. Nested hierarchy of meshes is generally assumed. Our approach utilizes a general two-level scheme, where the finite element space for the DG method is decomposed into a subspace (viewed as an auxiliary or 'coarse' space), plus a correction which can be handled by a standard smoothing procedure. We consider three different auxiliary subspaces, namely, piecewise linear C0-conforming functions, piecewise linear functions that are continuous at the centroids of the edges/faces (Crouzeix-Raviart finite elements) and piecewise constant functions over the finite elements. To support the theoretical results, we also present numerical experiments for 3-D model problem showing uniform convergence of the constructed methods.

Original languageEnglish (US)
Pages (from-to)753-770
Number of pages18
JournalNumerical Linear Algebra with Applications
Volume13
Issue number9
DOIs
StatePublished - Nov 1 2006

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Applied Mathematics

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