L1 scheme on graded mesh for subdiffusion equation with nonlocal diffusion term

Abstract

The solution of time fractional partial differential equations in general exhibit a weak singularity near the initial time. In this article we propose a method for solving time fractional diffusion equation with nonlocal diffusion term. The proposed method comprises L1 scheme on graded mesh, finite element method and Newton’s method. We discuss the well-posedness of the weak formulation at discrete level and derive a priori error estimates for fully-discrete formulation in L2(Ω) and H1(Ω) norms. Finally, some numerical experiments are conducted to validate the theoretical findings.