Volume 7, Issue 2
A New Finite Volume Method for the Stokes Problems

Int. J. Numer. Anal. Mod., 7 (2010), pp. 281-302.

Published online: 2010-07

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• 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.

• Keywords

Finite volume methods, Stokes problems, discontinuous Galerkin method.

Primary, 65N15, 65N30, 76D07, Secondary, 35B45, 35J50

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@Article{IJNAM-7-281, author = {}, title = {A New Finite Volume Method for the Stokes Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/720.html} }
TY - JOUR T1 - A New Finite Volume Method for the Stokes Problems JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 281 EP - 302 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/720.html KW - Finite volume methods, Stokes problems, discontinuous Galerkin method. AB -

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.

J. Wang, Y. Wang & X. Ye. (1970). A New Finite Volume Method for the Stokes Problems. International Journal of Numerical Analysis and Modeling. 7 (2). 281-302. doi:
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