论文标题
关于能量稳定，最大原则保存，二阶BDF方案，具有可变步骤
On energy stable, maximum-principle preserving, second order BDF scheme with variable steps for the Allen-Cahn equation
论文作者
论文摘要
在这项工作中，我们研究了两步的向后分化公式（BDF2），具有allen-cahn方程的不均匀网格。我们表明，在时间步长限制下，不均匀的BDF2方案是能稳定的$ r_k：=τ_k/τ_{k-1} <（3+ \ sqrt {17}）/2 \ 3.561。比率限制$ r_k <1+ \ sqrt {2} \大约2.414 $和实用的时间步长约束。还提出了最大规范中的二阶收敛速率。提供数值实验以支持理论发现。
In this work, we investigate the two-step backward differentiation formula (BDF2) with nonuniform grids for the Allen-Cahn equation. We show that the nonuniform BDF2 scheme is energy stable under the time-step ratio restriction $r_k:=τ_k/τ_{k-1}<(3+\sqrt{17})/2\approx3.561.$ Moreover, by developing a novel kernel recombination and complementary technique, we show, for the first time, the discrete maximum principle of BDF2 scheme under the time-step ratio restriction $r_k<1+\sqrt{2}\approx 2.414$ and a practical time step constraint. The second-order rate of convergence in the maximum norm is also presented. Numerical experiments are provided to support the theoretical findings.
