The study focuses on deriving optimal error estimates for time fractional PDEs and PIDEs using an IMEX-L1-FEM. The approach combines an IMEX-L1 method on graded mesh in the temporal direction with a finite element method in the spatial direction. The results include global almost optimal error estimates in L2- and H1-norms, even as α approaches 1−. The novelty lies in managing the interaction between the L1 approximation of the fractional derivative and the time discrete elliptic operator to achieve direct optimal estimates in H1-norm. Superconvergence results are established for 2D problems under specific conditions.
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by Aditi Tomar,... at arxiv.org 03-19-2024
https://arxiv.org/pdf/2302.05188.pdfDeeper Inquiries