论文标题
分析二阶BDF方案，其分子束外延模型具有可变步骤，而无需坡度选择
Analysis of the second order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection
论文作者
论文摘要
在这项工作中，我们关注二阶BDF（BDF2）方案的稳定性和收敛分析，该方案具有可变步骤，用于分子束外延模型，而无需坡度选择。我们首先证明可变阶段的BDF2方案是凸面，并且在弱的时步约束下可解决。 Then we show that it preserves an energy dissipation law if the adjacent time-step ratios $r_k:=τ_k/τ_{k-1}<3.561.$ Moreover, with a novel discrete orthogonal convolution kernels argument and some new discrete convolutional inequalities, the $L^2$ norm stability and rigorous error estimates are established, under the same step-ratios constraint that ensuring the energy稳定性。，即$ 0 <r_k <3.561。$这是文学中的最佳结果。我们最终采用了自适应时间步变策略来加速稳态解决方案的计算，并通过数值示例确认我们的理论发现。
In this work, we are concerned with the stability and convergence analysis of the second order BDF (BDF2) scheme with variable steps for the molecular beam epitaxial model without slope selection. We first show that the variable-step BDF2 scheme is convex and uniquely solvable under a weak time-step constraint. Then we show that it preserves an energy dissipation law if the adjacent time-step ratios $r_k:=τ_k/τ_{k-1}<3.561.$ Moreover, with a novel discrete orthogonal convolution kernels argument and some new discrete convolutional inequalities, the $L^2$ norm stability and rigorous error estimates are established, under the same step-ratios constraint that ensuring the energy stability., i.e., $0<r_k<3.561.$ This is known to be the best result in literature. We finally adopt an adaptive time-stepping strategy to accelerate the computations of the steady state solution and confirm our theoretical findings by numerical examples.
