articleMathematics of ComputationMay 5, 2014BRONZE OA

A weak Galerkin mixed finite element method for second order elliptic problems

JWJunping WangXYXiu Ye

U.S. National Science Foundation · Division of Mathematical Sciences · +1 more institution

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Abstract

A new weak Galerkin (WG) method is introduced and analyzed for the second order elliptic equation formulated as a system of two first order linear equations. This method, called WG-MFEM, is designed by using discontinuous piecewise polynomials on finite element partitions with arbitrary shape of polygons/polyhedra. The WG-MFEM is capable of providing very accurate numerical approximations for both the primary and flux variables. Allowing the use of discontinuous approximating functions on arbitrary shape of polygons/polyhedra makes the method highly flexible in practical computation. Optimal order error estimates in both discrete H 1 H^1 and L 2 L^2 norms are established for the corresponding…

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Topics & keywords

Topics
Keywords
  • Mathematics
  • Polyhedron
  • Finite element method
  • Discontinuous Galerkin method
  • Galerkin method
  • Piecewise linear function
  • Piecewise
  • Order (exchange)
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