Finite element analysis for coupled time-fractional nonlinear diffusion system

Abstract

This paper is concerned with the L1-Galerkin finite element analysis of the coupled time-fractional nonlinear diffusion system. Existence and uniqueness results are discussed at continuous as well as discrete levels. Two different methods for linearizing the nonlinear fully discrete problems are used. We provide a priori bounds and convergence estimates in L2(Ω) norm for fully-discrete problems. Numerical results based on the presented finite element methods are provided to validate the theoretical estimates.