TY - JOUR

T1 - An analysis of HDG methods for the vorticity-velocity-pressure formulation of the stokes problem in three dimensions

AU - Cockburn, Bernardo

AU - Cui, Jintao

PY - 2012

Y1 - 2012

N2 - 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 ≥ 0, the L2-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.

AB - 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 ≥ 0, the L2-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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U2 - 10.1090/S0025-5718-2011-02575-5

DO - 10.1090/S0025-5718-2011-02575-5

M3 - Article

AN - SCOPUS:84870852157

VL - 81

SP - 1355

EP - 1368

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 279

ER -