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 $L^2$-norm when the initial data $u_0\in H_0^1(\Omega)\cap H^2(\Omega)$. Additionally, an error estimate in $L^\infty$-norm is derived for 2D problems. All the derived estimates and bounds in this article remain valid as $\alpha\to 1^{-}$, where $\alpha$ 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.

翻译：本文研究了一类具有时空依赖系数及非自伴椭圆部分的时滞分数阶偏积分微分方程（PIDEs）的非均匀隐式-显式L1混合有限元方法（IMEX-L1-MFEM）。所提出的全离散方法将时间变量上基于分级网格的IMEX-L1方法与空间变量上的混合有限元方法相结合。研究的重点在于分析稳定性结果，并建立当初始数据$u_0\in H_0^1(\Omega)\cap H^2(\Omega)$时，解与通量在$L^2$范数下直至对数因子的最优误差估计。此外，针对二维问题推导了$L^\infty$范数下的误差估计。本文推导的所有估计和界在$\alpha\to 1^{-}$时均保持有效，其中$\alpha$为Caputo分数阶导数的阶数。最后，文末进行的若干数值实验结果验证了理论结论。