New Finite Element Methods in Computational Fluid Dynamics by H(div) Elements

Authors:
Junping Wang;Xiu Ye
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2007

Citing 0
Cited 9

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Abstract

In this paper, the authors present two formulations for the Stokes problem which make use of the existing $H({\rm div})$ elements of the Raviart-Thomas type originally developed for the second-order elliptic problems. In addition, two new $H({\rm div})$ elements are constructed and analyzed particularly for the new formulations. Optimal-order error estimates are established for the corresponding finite element solutions in various Sobolev norms. The finite element solutions feature a full satisfaction of the continuity equation when existing Raviart-Thomas-type elements are employed in the numerical scheme.