Stability and optimal convergence analysis of a non-uniform implicit-explicit L1 finite element method (IMEX-L1-FEM) are studied for a class of time-fractional linear partial differential/integro-differential equations with non-self-adjoint elliptic part having variable (space-time) coefficients. Non-uniform IMEX-L1-FEM is based on a combination of an IMEX-L1 method on graded mesh in the temporal direction and a finite element method in the spatial direction. A discrete fractional Gr\"{o}nwall inequality is proposed, which enables us to derive optimal error estimates in $L^2$- and $H^1$-norms. Numerical experiments are presented to validate our theoretical findings.

翻译：本文研究了一类具有变系数（时空相关）非自伴椭圆部分的时间分数阶线性偏微分/积分微分方程的非均匀隐式-显式L1有限元方法（IMEX-L1-FEM）的稳定性和最优收敛性分析。非均匀IMEX-L1-FEM基于时间方向上的分级网格IMEX-L1方法与空间方向上的有限元方法相结合。我们提出了一种离散分数阶Grönwall不等式，该不等式可用于推导$L^2$和$H^1$范数下的最优误差估计。数值实验验证了我们的理论结果。