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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

An analysis of HDG methods for the vorticity-velocity-pressure formulation of the Stokes problem in three dimensions


Authors: Bernardo Cockburn and Jintao Cui
Journal: Math. Comp. 81 (2012), 1355-1368
MSC (2010): Primary 65M60, 65N30, 35L65
Published electronically: December 21, 2011
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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$.


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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

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02575-5
PII: S 0025-5718(2011)02575-5
Keywords: Discontinuous Galerkin methods, hybridization, incompressible fluid flow
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.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.