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Title of Journal: Adv Comput Math

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Abbravation: Advances in Computational Mathematics

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Springer US

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10.1007/bf01898459

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1572-9044

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A weak Galerkin finite element method for the stok

Authors: Junping Wang Xiu Ye
Publish Date: 2015/05/23
Volume: 42, Issue: 1, Pages: 155-174
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Abstract

This paper introduces a weak Galerkin WG finite element method for the Stokes equations in the primal velocitypressure formulation This WG method is equipped with stable finite elements consisting of usual polynomials of degree k≥1 for the velocity and polynomials of degree k−1 for the pressure both are discontinuous The velocity element is enhanced by polynomials of degree k−1 on the interface of the finite element partition All the finite element functions are discontinuous for which the usual gradient and divergence operators are implemented as distributions in properlydefined spaces Optimalorder error estimates are established for the corresponding numerical approximation in various norms It must be emphasized that the WG finite element method is designed on finite element partitions consisting of arbitrary shape of polygons or polyhedra which are shape regularThe research of Wang was supported by the NSF IR/D program while working at the Foundation However any opinion finding and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation

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