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

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.

26 pages

References in corpus (2)

• A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation with Large Wave Numbers
• A Weak Galerkin Finite Element Method for Second-Order Elliptic Problems

Cited by in corpus (2)

• A Primal-Dual Weak Galerkin Finite Element Method for Fokker-Planck Type Equations
• An auxiliary space multigrid preconditioner for the weak Galerkin method