A weak Galerkin finite element method for the stokes equations
A weak Galerkin finite element method for the stokes equations
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DOI：
10.1007/s10444-015-9415-2
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发表时间：
2013-02
影响因子：
1.7
通讯作者：
Junping Wang;X. Ye
中科院分区：
文献类型：
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作者：
Junping Wang;X. Ye
本文介绍了一种求解速度-压力方程的弱Galerkin有限元方法。这种WG方法配备了稳定的有限元组成的通常多项式k ≥1的速度和多项式k −1的压力，两者都是不连续的。速度元素在有限元分区的界面上通过k-1次多项式增强。所有的有限元函数都是不连续的，通常的梯度和发散算子在适当定义的空间中被实现为分布。最优阶误差估计建立相应的数值逼近在各种规范。必须强调的是，WG有限元法是设计在由任意形状的多边形或多面体组成的有限元分区上的，这些多边形或多面体是形状规则的。
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 degreek≥1 for the velocity and polynomials of degreek−1 for the pressure, both are discontinuous. The velocity element is enhanced by polynomials of degreek−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.