Weak Galerkin finite element method with second-order accuracy in time for parabolic problems.

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]