Year: 2010
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 2 : pp. 281–302
Abstract
A new finite volume method for solving the Stokes equations is developed in this paper. The finite volume method makes use of the $BDM_1$ mixed element in approximating the velocity unknown, and consequently, the finite volume solution features a full satisfaction of the divergence-free constraint as required for the exact solution. Optimal-order error estimates are established for the corresponding finite volume solutions in various Sobolev norms. Some preliminary numerical experiments are conducted and presented in the paper. In particular, a post-processing procedure was numerically investigated for the pressure approximation. The result shows a superconvergence for a local averaging post-processing method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-IJNAM-720
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 2 : pp. 281–302
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Finite volume methods Stokes problems discontinuous Galerkin method.