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.
UR - http://www.scopus.com/inward/record.url?scp=84870852157&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84870852157&partnerID=8YFLogxK
U2 - 10.1090/S0025-5718-2011-02575-5
DO - 10.1090/S0025-5718-2011-02575-5
M3 - Article
AN - SCOPUS:84870852157
SN - 0025-5718
VL - 81
SP - 1355
EP - 1368
JO - Mathematics of Computation
JF - Mathematics of Computation
IS - 279
ER -