Unconditionally optimal convergence of a linearized Galerkin FEM for the nonlinear time-fractional mobile/immobile transport equation

In this paper, a linearized Galerkin finite element method (FEM) is discussed for solving the nonlinear time-fractional mobile/immobile transport equation. Utilizing the temporal- spatial error splitting argument, we derive the optimal L-2-norm error estimate without the stepsize restriction condition tau = O (h(d/4) ). The key point in our analysis is to obtain the unconditionally optimal error estimate between the solutions of the time-discrete system and continuous problem in H-2-norm, with which, we prove the boundedness of the fully discrete finite element solution in L-infinity-norm by using induction method. Then, the unconditionally optimal error estimate in L-2-norm can be obtained in the usual way. Finally, three numerical examples in both two and three dimensional spaces are given to illustrate the correctness of our theoretical analysis. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.