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 L²-norm error estimate without the stepsize restriction condition [Formula presented]. 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 H²-norm, with which, we prove the boundedness of the fully discrete finite element solution in L^∞-norm by using induction method. Then, the unconditionally optimal error estimate in L²-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.