Stabilizer-free weak Galerkin finite element method with second-order accuracy in time for the time fractional diffusion equation

Abstract

In this paper, we study a stabilizer-free weak Galerkin (SFWG) finite element method with second-order accuracy in time for solving time-fractional diffusion equation. We apply the SFWG finite element method to discretize the Laplace operator and the L2-1σ formula for the Caputo fractional derivative. Optimal convergence orders of semi-discrete scheme in L2 norm and H1 norm and fully discrete L2-1σ-SFWG scheme in L2 norm are obtained. Numerical experiments are performed to verify theoretical results.