In this study, we consider a class of non-autonomous time-fractional partial advection-diffusion-reaction (TF-ADR) equations with Caputo type fractional derivative. To obtain the numerical solution of the model problem, we apply the non-symmetric interior penalty Galerkin (NIPG) method in space on a uniform mesh and the L1-scheme in time on a graded mesh. It is demonstrated that the computed solution is discretely stable. Superconvergence of error estimates for the proposed method are obtained using the discrete energy-norm. Also, we have applied the proposed method to solve semilinear problems after linearizing by the Newton linearization process. The theoretical results are verified through numerical experiments.

翻译：本研究考虑了一类具有Caputo型分数阶导数的非自治时间分数阶偏对流-扩散-反应（TF-ADR）方程。为获得模型问题的数值解，我们在均匀网格上采用空间非对称内惩罚伽辽金（NIPG）方法，并在分级网格上采用时间L1格式。结果表明，计算解具有离散稳定性。通过离散能量范数，获得了所提方法的误差估计超收敛性。此外，我们将所提方法应用于牛顿线性化过程后的半线性问题求解。通过数值实验验证了理论结果。