A weak Galerkin finite element method for the stokes equations

被引：2
作者：
Junping Wang
Xiu Ye
机构：
[1] University of Arkansas at Little Rock,Department of Mathematics
[2] National Science Foundation,Division of Mathematical Sciences
来源：
Advances in Computational Mathematics | 2016年 / 42卷
关键词：
Weak Galerkin; Finite element methods; The stokes equations; Polyhedral meshes; Primary; 65N15; 65N30; 76D07; Secondary; 35B45; 35J50;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper introduces a weak Galerkin (WG) finite element method for the Stokes equations in the primal velocity-pressure 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 properly-defined spaces. Optimal-order 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 regular.
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页码：155 / 174
页数：19
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