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June  2006, 5(2): 349-365. doi: 10.3934/cpaa.2006.5.349

Abstract cascading multigrid preconditioners in Besov spaces

Hermann Brunner 1, and  Jingtang Ma 2,

1. 

Dept. of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, Canada A1C 5S7
2. 

Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100080, China

Received  April 2005 Revised  August 2005 Published  March 2006

In this paper we describe and analyze the general framework of cascading multigrid preconditioning. In particular, we introduce two preconditioners based on the cascading multigrid approach. We then illustrate the application of the corresponding method to the heat equation with mild regularity in Besov spaces. Furthermore, we analyze a cascading multigrid preconditioner for the interior penalty discontinuous Galerkin method.
Keywords: discontinuous Galerkin method., Cascading multigrid method, preconditioner, finite element method, Besov spaces.
Mathematics Subject Classification: 65F10, 65N55, 65N30, 65R2.
Citation: Hermann Brunner, Jingtang Ma. Abstract cascading multigrid preconditioners in Besov spaces. Communications on Pure and Applied Analysis, 2006, 5 (2) : 349-365. doi: 10.3934/cpaa.2006.5.349
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