Article

hp-version interior penalty DGFEMs for the biharmonic equation

University of Oxford, Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK; Federal University of Santa Catarina, Mathematics Department, Trindade, Florianópolis, SC, 88040-900, Brazil
Computer Methods in Applied Mechanics and Engineering DOI:10.1016/j.cma.2006.06.014 pp.1851-1863

ABSTRACT We construct hp-version interior penalty discontinuous Galerkin finite element methods (DGFEMs) for the biharmonic equation, including symmetric and nonsymmetric interior penalty discontinuous Galerkin methods and their combinations: semisymmetric methods. Our main concern is to establish the stability and to develop the a priori error analysis of these methods. We establish error bounds that are optimal in h and slightly suboptimal in p. The theoretical results are confirmed by numerical experiments.

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Keywords

biharmonic equation
 
DGFEMs
 
error bounds
 
hp-version interior penalty discontinuous Galerkin finite element methods
 
main concern
 
nonsymmetric interior penalty discontinuous Galerkin methods
 
priori error analysis
 
theoretical results