Divergence-Free HDG Methods for the Vorticity-Velocity Formulation of the Stokes Problem |
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Authors: | Bernardo Cockburn Jintao Cui |
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Affiliation: | 1. School of Mathematics, University of Minnesota, 206 Church St. SE, Minneapolis, MN, 55455, USA 2. Institute for Mathematics and Its Applications, University of Minnesota, 114 Lind Hall, 207 Church St. SE, Minneapolis, MN, 55455, USA
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Abstract: | We study a hybridizable discontinuous Galerkin method for solving the vorticity-velocity formulation of the Stokes equations in three-space dimensions. We show how to hybridize the method to avoid the construction of the divergence-free approximate velocity spaces, recover an approximation for the pressure and implement the method efficiently. We prove that, when all the unknowns use polynomials of degree k??0, the L 2 norm of the errors in the approximate vorticity and pressure converge with order k+1/2 and the error in the approximate velocity converges with order k+1. We achieve this by letting the normal stabilization function go to infinity in the error estimates previously obtained for a hybridizable discontinuous Galerkin method. |
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