Journal
MATHEMATICS OF COMPUTATION
Volume 83, Issue 289, Pages 2101-2126Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0025-5718-2014-02852-4
Keywords
Weak Galerkin; finite element methods; discrete weak divergence; second order elliptic problems; mixed finite element methods
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Funding
- NSF IR/D program
- National Science Foundation [DMS-1115097]
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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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