The Weak Galerkin Finite Element Method for Solving the Time-Dependent Integro-Differential Equations

Abstract

In this paper, we solve linear parabolic integral differential equations using the weak Galerkin finite element method (WG) by adding a stabilizer. The semi-discrete and fully-discrete weak Galerkin finite element schemes are constructed. Optimal convergent orders of the solution of the WG in $L^2$ and $H^1$ norm are derived. Several computational results confirm the correctness and efficiency of the method.