A Weak Galerkin Method with $C^0$ Element for Fourth Order Linear Parabolic Equation

Abstract

This paper is concerned with the $C^0$ weak Galerkin finite element method for a fourth order linear parabolic equation. The method is based on the construction of a discrete weak Laplacian operator. The error estimates are obtained for semi-discrete weak Galerkin finite element method. Numerical results are presented to confirm the theory.