277 RWTH Publication No: 47246        2007        IGPM277.pdf
TITLE A Multilevel Preconditioner for the Interior Penalty Discontinuous Galerkin Method
AUTHORS Kolja Brix, Martin Campos Pinto, Wolfgang Dahmen
ABSTRACT In this article we present a multilevel preconditioner for interior penalty discontinuous Galerkin discretizations of second order elliptic boundary value problems that gives rise to uniformly bounded condition numbers without any additional regularity assumptions on the solution. The underlying triangulations are only assumed to be shape regular but may have hanging nodes subject to certain mild grading conditions. A key role is played by certain decompositions of the discontinuous trial space into a conforming subspace and a non-conforming subspace that is controlled by the jumps across the edges.
KEYWORDS interior penalty method, energy-stable splittings, admissible averaging operators, frames, multilevel Schwarz preconditioners, discontinuous Galerkin methods
DOI 10.1137/07069691X
PUBLICATION SIAM Journal on Numerical Analysis
Volume 46, Issue 5, pp. 2742-2768, 2008