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Superconvergence and H(div) projection for discontinuous Galerkin methods
Author(s) -
Bastian Peter,
Rivière Béatrice
Publication year - 2003
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.562
Subject(s) - superconvergence , discontinuous galerkin method , projection (relational algebra) , mathematics , galerkin method , convergence (economics) , flow (mathematics) , conservation of mass , property (philosophy) , projection method , mathematical analysis , finite element method , mathematical optimization , geometry , mechanics , physics , algorithm , dykstra's projection algorithm , philosophy , epistemology , economics , thermodynamics , economic growth
We introduce and analyse a projection of the discontinuous Galerkin (DG) velocity approximations that preserve the local mass conservation property. The projected velocities have the additional property of continuous normal component. Both theoretical and numerical convergence rates are obtained which show that the accuracy of the DG velocity field is maintained. Superconvergence properties of the DG methods are shown. Finally, numerical simulations of complicated flow and transport problem illustrate the benefits of the projection. Copyright © 2003 John Wiley & Sons, Ltd.