论文标题
兼容的$ l^2 $适用于斜率选择的时间分数MBE Mobel的可变步骤L1方案的范围融合
Compatible $L^2$ norm convergence of variable-step L1 scheme for the time-fractional MBE mobel with slope selection
论文作者
论文摘要
研究了可变步长L1方案的收敛性，用于使用斜率选择的时间分子束外延（MBE）模型。一种新型的渐近兼容$ l^2 $ n r^2 $规范误差估计值在可变性稳定性稳定性稳定性（CSS）-consistentimistectimenteptep pientepthrent下建立。 CSS一致的条件意味着收敛所需的最大台阶限制与可溶解性和稳定性（在某些规范中）的顺序相同。据我们所知，这是第一次为非线性次扩散问题建立此类错误估计。渐近兼容的收敛意味着，误差估计与经典MBE模型的后向Euler方案兼容，作为分数顺序$α\ rightarrow 1^ - $。正如向后的Euler方案可以维持MBE方程的物理特性一样，可变步骤L1方案还可以保留时间分数MBE模型的相应性能，包括音量保守，变异能量耗散法和$ l^2 $ norm限制。提出了数值实验以支持我们的理论结果。
The convergence of variable-step L1 scheme is studied for the time-fractional molecular beam epitaxy (MBE) model with slope selection.A novel asymptotically compatible $L^2$ norm error estimate of the variable-step L1 scheme is established under a convergence-solvability-stability (CSS)-consistent time-step constraint. The CSS-consistent condition means that the maximum step-size limit required for convergence is of the same order to that for solvability and stability (in certain norms) as the small interface parameter $ε\rightarrow 0^+$. To the best of our knowledge, it is the first time to establish such error estimate for nonlinear subdiffusion problems. The asymptotically compatible convergence means that the error estimate is compatible with that of backward Euler scheme for the classical MBE model as the fractional order $α\rightarrow 1^-$. Just as the backward Euler scheme can maintain the physical properties of the MBE equation, the variable-step L1 scheme can also preserve the corresponding properties of the time-fractional MBE model, including the volume conservation, variational energy dissipation law and $L^2$ norm boundedness. Numerical experiments are presented to support our theoretical results.
