4.4 Article

Error estimates for Galerkin finite element approximations of time-fractional nonlocal diffusion equation

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Summary: This study investigates a time-fractional diffusion equation involving Dirichlet energy, with a nonlocal diffusion operator in spatial dimensions d belonging to {2,3} and a Caputo sense fractional derivative in time. Discretization is done using Galerkin finite elements in space and finite difference scheme in time, with the existence and uniqueness of a fully discrete numerical solution proved using the Brouwer fixed point theorem. The proposed scheme demonstrates second order convergence, supported by a priori bounds and convergence estimates in L-2 and L-infinity norms for the fully discrete problem. Numerical results further validate the theoretical analysis.

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