A fully discrete two-grid modified method of characteristics (MMOC) scheme is proposed for nonlinear variable-order time-fractional advection–diffusion equations in two space dimensions. The MMOC is used to handle the advection-dominated transport and the two-grid method is designed for efficiently solving the resulting nonlinear system. Optimal $L^2$ error estimates are derived for both the MMOC scheme and the corresponding two-grid MMOC scheme. Numerical experiments are presented to demonstrate the accuracy and the efficiency of the proposed method.

中文翻译：

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非线性变阶时间分数阶移动/不动对流扩散方程的两网格MMOC有限元方法

针对二维空间中的非线性变阶时间分数维对流扩散方程，提出了一种完全离散的两网格特征修正方法（MMOC）。MMOC用于处理以对流为主的输运，而两网格方法旨在有效地解决所得的非线性系统。最佳${\mathrm{大号}}^2$对于MMOC方案和相应的两网格MMOC方案，都得出了误差估计。数值实验表明了该方法的准确性和有效性。