A Robust Numerical Method for Stokes Equations Based on Divergence-Free $H$(div) Finite Element Methods

Authors:
Junping Wang;Yanqiu Wang;Xiu Ye
Affiliations:
jwang@nsf.gov;yqwang@math.okstate.edu;xxye@ualr.edu
Venue:
SIAM Journal on Scientific Computing
Year:
2009

Citing 0
Cited 3

An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations

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A Posteriori Error Estimation for an Interior Penalty Type Method Employing $H(\mathrm{div})$ Elements for the Stokes Equations

SIAM Journal on Scientific Computing
Penalty-Factor-Free Discontinuous Galerkin Methods for 2-Dim Stokes Problems

SIAM Journal on Numerical Analysis

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Abstract

A computational method based on a divergence-free $H$(div) approach is presented for the Stokes equations in this article. This method is designed to find velocity approximation in an exact divergence-free subspace of the corresponding $H$(div) finite element space. That is, the continuity equation is strongly enforced a priori and the pressure is eliminated from the linear system in calculation. A strength of this approach is that the saddle-point problem for Stokes equations is reduced to a symmetric positive definite problem in a subspace for which basis functions are readily available. The resulting discrete system can then be solved by using existing sophisticated solvers. The aim of this article is to demonstrate the efficiency and robustness of $H$(div) finite element methods for Stokes equations. The results not only confirm the existing theoretical results but also reveal additional advantages of the method in dealing with discontinuous boundary conditions.