Preconditioning of symmetric interior penalty discontinuous galerkin FEM for elliptic problems

Veselin A. Dobrev, Raytcho D. Lazarov, Ludmil T. Zikatanov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

This is a further development of [9] regarding multilevel preconditioning for symmetric interior penalty discontinuous Galerkin finite element approximations of second order elliptic problems. We assume that the mesh on the finest level is a results of a geometrically refined fixed coarse mesh. The preconditioner is a multilevel method that uses a sequence of finite element spaces of either continuous or piecewise constant functions. The spaces are nested, but due to the penalty term in the DG method the corresponding forms are not inherited. For the continuous finite element spaces we show that the variable V-cycle provides an optimal preconditioner for the DG system. The piece-wise constant functions do not have approximation property so in order to control the energy growth of the inter-level transfer operator we apply W-cycle MG. Finally, we present a number of numerical experiments that support the theoretical findings.

Original languageEnglish (US)
Title of host publicationDomain Decomposition Methods in Science and Engineering XVII
Pages33-44
Number of pages12
DOIs
StatePublished - Dec 1 2008
Event17th International Conference on Domain Decomposition Methods - St. Wolfgang /Strobl, Austria
Duration: Jul 3 2006Jul 7 2006

Publication series

NameLecture Notes in Computational Science and Engineering
Volume60
ISSN (Print)1439-7358

Other

Other17th International Conference on Domain Decomposition Methods
CountryAustria
CitySt. Wolfgang /Strobl
Period7/3/067/7/06

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

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    Dobrev, V. A., Lazarov, R. D., & Zikatanov, L. T. (2008). Preconditioning of symmetric interior penalty discontinuous galerkin FEM for elliptic problems. In Domain Decomposition Methods in Science and Engineering XVII (pp. 33-44). (Lecture Notes in Computational Science and Engineering; Vol. 60). https://doi.org/10.1007/978-3-540-75199-1_3