Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations Academic Article uri icon

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. Copyright 2006 John Wiley & Sons, Ltd.

published proceedings

  • NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS

author list (cited authors)

  • Dobrev, V. A., Lazarov, R. D., Vassilevski, P. S., & Zikatanov, L. T.

citation count

  • 54

complete list of authors

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

publication date

  • January 2006

publisher