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Discontinuous Galerkin approximations of the Stokes and Navier-Stokes equations

Authors: Konstantinos Chrysafinos and Noel J. Walkington
Journal: Math. Comp. 79 (2010), 2135-2167
MSC (2010): Primary 65M12, 65M60
Published electronically: April 14, 2010
MathSciNet review: 2684359
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Abstract: Numerical schemes to compute approximate solutions of the evolutionary Stokes and Navier-Stokes equations are studied. The schemes are discontinuous in time and conforming in space and of arbitrarily high order. Fully-discrete error estimates are derived and dependence of the viscosity constant is carefully tracked. It is shown that the errors are bounded by projection errors of the exact solution which exhibit optimal rates when the solutions are smooth.

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Additional Information

Konstantinos Chrysafinos
Affiliation: Department of Mathematics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, Zografou Campus, Athens 15780, Greece

Noel J. Walkington
Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

Keywords: Navier Stokes, Discontinuous Time Stepping
Received by editor(s): May 16, 2009
Received by editor(s) in revised form: March 26, 2009
Published electronically: April 14, 2010
Additional Notes: This work was supported in part by National Science Foundation Grant DMS–0811029. This work was also supported by the NSF through the Center for Nonlinear Analysis.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.