Weak Galerkin Finite Element Methods for Second-Order Elliptic Problems on Polytopal Meshes

Details Weak Galerkin Finite Element Methods for Second-Order Elliptic Problems on Polytopal Meshes Weak Galerkin Finite Element Methods for Second-Order Elliptic Problems on Polytopal Meshes

2012-04-16

arxiv.org/abs/1204.3655v1

Mathematics

Numerical Analysis

16 pages, 3 figures, 4 tables

Scientific paper

A new weak Galerkin (WG) finite element method is introduced and analyzed for the second order elliptic equation in this paper. This method, called WG-FEM, is designed by using discontinuous piecewise polynomials on finite element partitions with arbitrary polytopes with certain shape regularity. Allowing the use of discontinuous approximating functions on arbitrary polytopal elements is a highly demanded feature for numerical algorithms in scientific computing. Optimal order error estimates are established for the corresponding WG-FEM approximations in both a discrete $H^1$ norm and the standard $L^2$ norm. Numerical results are reported to demonstrate the robustness, reliability, and accuracy of the WG-FEM for the underlying PDEs.

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