What question did this study set out to answer?

To develop a second-order numerical scheme for coupled time-fractional nonlocal diffusion problems and establish error estimates.

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April 10, 2026Open Access

Fractional Crank-Nicolson Galerkin FEM for Coupled Time-Fractional Nonlocal Parabolic Problems

Key Points

To develop a second-order numerical scheme for coupled time-fractional nonlocal diffusion problems and establish error estimates.
Introduced a fractional Crank-Nicolson method combined with Galerkin FEM and Newton’s method.
Establishing error estimates in L2 and H1_0 norms for the numerical solution.
Provided verification of theoretical estimates using standard FEM results.
Establishes a priori error estimates for the numerical method.
Verifies the effectiveness of the proposed scheme through comparison with standard finite element methods.

Abstract

In this paper, we introduce a second-order numerical scheme designed for addressing a coupled time-fractional nonlocal diffusion problem. The scheme is composed of the fractional Crank-Nicolson method integrated with the Galerkin finite element method (FEM) and Newton’s method. We establish a priori error estimates for a fully-discrete solution in L2 and \ (H¹₀\) norms. Additionally, we provide results based on the standard FEM to verify the theoretical estimates.

Fractional Crank-Nicolson Galerkin FEM for Coupled Time-Fractional Nonlocal Parabolic Problems

Key Points

Abstract

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