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arXiv · 1610.05355

A simple finite element method for the Stokes equations

Lin Mu·Xiu Ye
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Abstract

The goal of this paper is to introduce a simple finite element method to solve the Stokes and the Navier-Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate and robust.

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Lin Mu, Xiu Ye. 2016-10-17. A simple finite element method for the Stokes equations. https://arxiv.org/abs/1610.05355

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