Abstract

In this article, a local discontinuous Galerkin (LDG) method is studied for numerically solving the fractal mobile/immobile transport equation with a new time Caputo–Fabrizio fractional derivative. The stability of the LDG scheme is proven, and a priori error estimates with the second‐order temporal convergence rate and the (k + 1)th order spatial convergence rate are derived in detail. Finally, numerical experiments based on Pk, k = 0, 1, 2, 3, elements are provided to verify our theoretical results.

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