Abstract
The goal of this paper is to introduce a simple finite element method to solve the 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.
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Acknowledgments
The first author’s research is based upon work supported in part by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under award number ERKJE45; and by the Laboratory Directed Research and Development program at the Oak Ridge National Laboratory, which is operated by UT-Battelle, LLC., for the U.S. Department of Energy under Contract DE-AC05-00OR22725. This research was supported in part by National Science Foundation Grant DMS-1620016.
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Communicated by: Long Chen
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Mu, L., Ye, X. A simple finite element method for the Stokes equations. Adv Comput Math 43, 1305–1324 (2017). https://doi.org/10.1007/s10444-017-9526-z
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DOI: https://doi.org/10.1007/s10444-017-9526-z