A weak Galerkin finite element method for the stokes equations

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• 作者：Junping Wang ; Xiu Ye
• 关键词：Weak Galerkin ; Finite element methods ; The stokes equations ; Polyhedral meshes ; Primary ; 65N15 ; 65N30 ; 76D07 ; Secondary ; 35B45 ; 35J50
• 刊名：Advances in Computational Mathematics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：42
• 期：1
• 页码：155-174
• 全文大小：358 KB
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• 作者单位：Junping Wang (1)
  Xiu Ye (2)
  
  1. Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA
  2. Division of Mathematical Sciences, National Science Foundation, Arlington, VA, 22230, USA
  
• 刊物类别：Computer Science
• 刊物主题：Numeric Computing
  Calculus of Variations and Optimal Control
  Mathematics
  Algebra
  Theory of Computation
  
• 出版者：Springer U.S.
• ISSN：1572-9044

文摘

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. Keywords Weak Galerkin Finite element methods The stokes equations Polyhedral meshes