Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

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
Posted: 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 -norm of the errors in the approximate vorticity and pressure converge to zero with order , whereas the error in the approximate velocity converges with order .

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