Research Highlights

a-Robust Error Analysis of L2-1r Scheme on Graded Mesh for Time-Fractional Nonlocal Diffusion Equation

Authors :- Kundaliya P.J.

Publication :- Journal of Computational and Nonlinear Dynamics, 19(5): 051004, ASME, 2024

In this work, a time-fractional nonlocal diffusion equation is considered. Based on the L2-σ scheme on a graded mesh in time and the standard finite element method (FEM) in space, the fully-discrete L2-σ finite element method is investigated for a time-fractional nonlocal diffusion problem. We prove the existence and uniqueness of fully-discrete solution. The α-robust error bounds are derived, i.e., bounds remain valid as α where α is the order of a temporal fractional derivative. The numerical experiments are presented to justify the theoretical findings.