Errors of an Implicit Variable-Step BDF2 Method for a Molecular Beam Epitaxial Model with Slope Selection
Year: 2023
Author: Xuan Zhao, Haifeng Zhang, Hong Sun
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 4 : pp. 886–913
Abstract
Unconditionally stable and convergent variable-step BDF2 scheme for solving the MBE model with slope selection is derived. Discrete orthogonal convolution kernels of the variable-step BDF2 method are commonly utilized for solving the phase field models. We present new inequalities, concerning the vector forms, for the kernels especially dealing with nonlinear terms in the slope selection model. The convergence rate of the fully discrete scheme is proved to be two both in time and space in $L^2$ norm under the setting of the variable time steps. Energy dissipation law is proved rigorously with a modified energy by adding a small term to the discrete version of the original free energy functional. Two numerical examples including an adaptive time-stepping strategy are given to verify the convergence rate and the energy dissipation law.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2022-286.271222
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 4 : pp. 886–913
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Molecular beam epitaxial growth slope selection variable-step BDF2 scheme energy stability convergence.
Author Details
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Energy dissipation law of the variable time-step fractional BDF2 scheme for the time fractional molecular beam epitaxial model
Zhao, Xuan
Jiang, Zhuhan
Sun, Hong
International Journal of Computer Mathematics, Vol. 101 (2024), Iss. 9-10 P.1188
https://doi.org/10.1080/00207160.2024.2315131 [Citations: 1]