Linearized transformed [formula omitted] finite element methods for semi-linear time-fractional parabolic problems

Abstract

A linearized Galerkin finite element method is presented for numerically solving the semi-linear time-fractional parabolic problems, whose solutions always display a initial weak singularity. The transformed L1 scheme based on a change of variable is used to approximate Caputo derivatives and the finite element approximations to the spatial variables. By the temporal-spatial error splitting argument, unconditionally optimal error estimates of the proposed schemes are proved. Finally, several numerical experiments are given to demonstrate our theoretical results.