Discontinuous Galerkin approximations of the Stokes and Navier-Stokes equations
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- by Konstantinos Chrysafinos and Noel J. Walkington PDF
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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.References
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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
- Email: chrysafinos@math.ntua.gr
- Noel J. Walkington
- Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
- Email: noelw@andrew.cmu.edu
- 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.
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 79 (2010), 2135-2167
- MSC (2010): Primary 65M12, 65M60
- DOI: https://doi.org/10.1090/S0025-5718-10-02348-3
- MathSciNet review: 2684359