α-Robust Error Analysis of L2-1_σ Scheme on Graded Mesh for Time-fractional Nonlocal Diffusion Equation
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In this work, a time-fractional nonlocal diffusion equation is considered. Based on the L2-1_σ scheme on a graded mesh in time and the standard finite element method (FEM) in space, the fully-discrete L2-1_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 →1^-, where α ∈ (0,1) is the order of a temporal fractional derivative. The numerical experiments are presented to justify the theoretical findings.
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