A new finite volume method for the Stokes problems
Junping Wang 1, Yanqiu Wang 2, Xiu Ye 31 Division of Mathematical Sciences, National Science Foundation, Arlington, VA 22230, USA.
2 Department of Mathematics, Oklahoma State University, Stillwater, OK 74075, USA.
3 Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR 72204, USA.
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.
AMS subject classifications: 65N15, 65N30, 76D07, 35B45, 35J50
Key words: Finite volume methods, Stokes problems, discontinuous Galerkin method.
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