On $L^2$ Error Estimate for Weak Galerkin Finite Element Methods for Parabolic Problems

Abstract

A weak Galerkin finite element method with stabilization term, which is symmetric, positive definite and parameter free, was proposed to solve parabolic equations by using weakly defined gradient operators over discontinuous functions. In this paper, we derive the optimal order error estimate in $L^2$ norm based on dual argument. Numerical experiment is conducted to confirm the theoretical results.