TY - JOUR
T1 - A New Finite Volume Method for the Stokes Problems
AU - J. Wang, Y. Wang & X. Ye
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 - <p style="text-align: justify;">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.</p>