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

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

2012-02-16

arxiv.org/abs/1202.3655v1

Mathematics

Numerical Analysis

24 pages

Scientific paper

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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