Convergence analysis of time-filtered backward differentiation methods up to fourth-order for the molecular beam epitaxial model without slope selection
IF 2.6
3区 数学
Q2 MATHEMATICS, APPLIED
引用次数: 0
Abstract
This work presents the convergence of time-filtered backward differentiation formula (BDF) methods up to fourth-order time accuracy for the molecular beam epitaxial (MBE) equation without slope selection. With the help of the discrete orthogonal convolution kernels, some concise \(L^2\) norm error estimates are established via the discrete energy technique. To the best of our knowledge, this is the first time such type \(L^2\) norm error estimates of time-filtered BDF2 and time-filtered BDF3 schemes are obtained for a nonlinear parabolic equation. Numerical examples are included to show the effectiveness of the proposed methods.
无坡度选择的分子束外延模型四阶时间滤波后向微分法的收敛性分析
This work presents the convergence of time-filtered backward differentiation formula (BDF) methods up to fourth-order time accuracy for the molecular beam epitaxial (MBE) equation without slope selection. With the help of the discrete orthogonal convolution kernels, some concise L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document} norm error estimates are established via the discrete energy technique. To the best of our knowledge, this is the first time such type L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document} norm error estimates of time-filtered BDF2 and time-filtered BDF3 schemes are obtained for a nonlinear parabolic equation. Numerical examples are included to show the effectiveness of the proposed methods.
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来源期刊
CiteScore
3.00
自引率
5.90%
发文量
68
审稿时长
3 months
期刊介绍：
Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis.
This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.
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