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In this paper, we study a modified weak Galerkin finite element method (MWG-FEM) on anisotropic triangular meshes for a class of parabolic equations. Different from conventional weak Galerkin methods, the MWG-FEM replaces the boundary functions by the average of interior functions, which possesses flexibility in the approximation functions and mesh generation. Moreover, MWG-FEM is compatible with anisotropic meshes and suitable for solving problems with anisotropic property. By using the anisotropic interpolation and projection operators, the optimal order error estimate in L 2 norm is derived. Numerical experiments are performed to demonstrate the stability and efficiency of the method. [ABSTRACT FROM AUTHOR]

Abstract In this paper we study a weak Galerkin finite element method (WG-FEM) with second-order accuracy in time for solving one type of parabolic equations. We apply a discrete weak gradient operator on discontinuous piecewise polynomials in the numerical scheme. Fully-discrete WG finite element scheme is introduced and analyzed. Optimal order error estimates are derived in the L 2 norm. Numerical experiments are performed to verify the theoretical results. [ABSTRACT FROM AUTHOR]