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

Wang, Junping; Ye, Xiu

doi:10.1090/S0025-5718-2014-02852-4

A weak Galerkin mixed finite element method for second order elliptic problems
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by Junping Wang and Xiu Ye PDF

Math. Comp. 83 (2014), 2101-2126 Request permission

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 $H^1$ and $L^2$ norms are established for the corresponding weak Galerkin mixed finite element solutions.

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