Unconditionally convergent and superconvergent FEMs for nonlinear coupled time-fractional prey-predator problem

In this paper, a linearized L 1-Galerkin finite element method (FEM) is proposed to solve the nonlinear coupled time-fractional prey-predator problem. In order to derive the unconditionally optimal L-2-norm error estimate of the numerical scheme, the time-space error splitting technique is utilized in the convergence analysis. In addition, the unconditional superclose and superconvergence results under the bilinear finite element are deduced in details. To numerically solve the system with nonsmooth solutions and improve computational efficiency, we utilize nonuniform L1 scheme in time and construct the corresponding fast algorithm based on sum-of-exponentials technique. Finally, numerical examples are reported to show the accuracy of the proposed FEMs and the effectiveness of the fast algorithm.

Automated summary

In this paper, a linearized L 1-Galerkin finite element method is proposed to solve the nonlinear coupled time-fractional prey-predator problem. The time-space error splitting technique is utilized in the convergence analysis to derive the unconditionally optimal L-2-norm error estimate of the numerical scheme. Additionally, the unconditional superclose and superconvergence results under the bilinear finite element are deduced in detail. Numerical examples are presented to demonstrate the accuracy of the proposed FEMs and the effectiveness of the fast algorithm.