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arXiv · 1202.3655

A Weak Galerkin Mixed Finite Element Method for Second-Order Elliptic Problems

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

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Junping Wang, Xiu Ye. 2012-02-16. A Weak Galerkin Mixed Finite Element Method for Second-Order Elliptic Problems. https://arxiv.org/abs/1202.3655

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