Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection

• 作者: Hong-Lin Liao Xuehua Song Tao Tang Tao Zhou
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（5）
• 所属期刊栏目: Progress of Projects Supported by NSFC
• 页码范围: 887-902
• 页数: 16页
• 语种: 英文

摘要

In this work,we are concerned with the stability and convergence analysis of the second-order backward difference formula (BDF2) 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 satisfy rk :=τk/τk-1 ＜ 3.561.Moreover,with a novel discrete orthogonal convolution kernels argument and some new estimates on the corresponding positive definite quadratic forms,the L2 norm stability and rigorous error estimates are established,under the same step-ratio constraint that ensures the energy stability,i.e.,0 ＜ rk ＜ 3.561.This is known to be the best result in the 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.