An analysis of HDG methods for the vorticity-velocity-pressure formulation of the Stokes problem in three dimensions
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Abstract:
We provide the first a priori error analysis of a hybridizable discontinuous Galerkin (HDG) method for solving the vorticity-velocity-pressure formulation of the three-dimensional Stokes equations of incompressible fluid flow. By using a projection-based approach, we prove that, when all the unknowns use polynomials of degree $k\ge 0$, the $L^2$-norm of the errors in the approximate vorticity and pressure converge to zero with order $k+1/2$, whereas the error in the approximate velocity converges with order $k+1$.References
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Additional Information
- Bernardo Cockburn
- Affiliation: School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota 55455
- Email: cockburn@math.umn.edu
- Jintao Cui
- Affiliation: Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, Minnesota 55455
- Email: jcui@ima.umn.edu
- Received by editor(s): March 8, 2011
- Received by editor(s) in revised form: May 25, 2011
- Published electronically: December 21, 2011
- Additional Notes: The first author was partially supported by the National Science Foundation (Grant DMS-0712955) and by the Minnesota Supercomputing Institute.
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 1355-1368
- MSC (2010): Primary 65M60, 65N30, 35L65
- DOI: https://doi.org/10.1090/S0025-5718-2011-02575-5
- MathSciNet review: 2904582