CRPC-TR99799						September 1999

Title: Improved Energy Estimates for Interior Penalty, Constrained and
Discontinuous Galerkin Methods for Elliptical Problems

Authors: Beatrice Riviere, Mary Wheeler, and Vivette Girault

Submitted November 1999

Abstract:

     Three Galerkin methods using discontinuous approximation spaces are
introduced to solve elliptical problems.  The underlying bilinear form for
all three methods is the same and is nonsymmetric.  In one case, a penalty
is added to the form and in another, a constraint on jumps on each face of
the triangulation.  All three methods are locally conservative and the
third one is not restricted.  Optimal a priori hp error estimates are
derived for all three procedures.

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Beatrice Riviere and Mary Wheeler
The Center for Subsurface Modeling
The University of Texas

Vivette Girault
Universite Pierre et Marie Curie, Paris VI
Laboratoire Analyse Numerique
Paris, France