On a non-uniform $$\alpha $$-robust IMEX-L1 mixed FEM for time-fractional PIDEs

• Published in: Advances in computational mathematics Vol. 51; no. 1
• Main Authors: Tripathi, Lok Pati, Tomar, Aditi, Pani, Amiya K.
• Format: Journal Article
• Language: English
• Published: New York Springer Nature B.V 01.02.2025
• Subjects: Differential equations; Error analysis; Estimates; Finite element method; Mathematics; Time dependence
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-025-10221-3

A non-uniform implicit-explicit L1 mixed finite element method (IMEX-L1-MFEM) is investigated for a class of time-fractional partial integro-differential equations (PIDEs) with space-time-dependent coefficients and non-self-adjoint elliptic part. The proposed fully discrete method combines an IMEX-L1 method on a graded mesh in the temporal variable with a mixed finite element method in spatial variables. The focus of the study is to analyze stability results and to establish optimal error estimates, up to a logarithmic factor, for both the solution and the flux in L2-norm when the initial data u0∈H01(Ω)∩H2(Ω). Additionally, an error estimate in L∞-norm is derived for 2D problems. All the derived estimates and bounds in this article remain valid as α→1-, where α is the order of the Caputo fractional derivative. Finally, the results of several numerical experiments conducted at the end of this paper are confirming our theoretical findings.