Linearized transformed L1 finite element methods for semi-linear time-fractional parabolic problems

Yuxin Han, Xin Huang, Wei Gu and Bolong Zheng

Applied Mathematics and Computation, 2023, vol. 458, issue C

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.

Keywords: Nonlinear time fractional parabolic equation; Transformed L1 scheme; Linearized Galerkin finite element method; Unconditional convergence (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323004113

DOI: 10.1016/j.amc.2023.128242

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