A space--time discontinuous Galerkin method for the time-dependent Oseen equations

Authors:
J. J. W. van der Vegt;J. J. Sudirham
Affiliations:
Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands;Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands
Venue:
Applied Numerical Mathematics
Year:
2008

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Abstract

A space-time discontinuous Galerkin finite element method for the Oseen equations on time-dependent flow domains is presented. The algorithm results in a higher order accurate conservative discretization on moving and deforming meshes and is well suited for hp-adaptation. A detailed analysis of the stability of the numerical discretization is given which shows that the algorithm is unconditionally stable, also when equal order polynomial basis functions for the pressure and velocity are used. The accuracy of the space-time discretization is investigated using a detailed hp-error analysis and computations on a model problem.