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A Second Order Energy Stable BDF Numerical Scheme for the Swift–Hohenberg Equation

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Abstract

In this paper, we propose and analyze a second-order energy stable numerical scheme for the Swift–Hohenberg equation, with a mixed finite element approximation in space. We employ second-order backward differentiation formula scheme with a second-order stabilized term, which guarantees the long time energy stability. We prove that our two-step scheme is unconditionally energy stable and uniquely solvable. Furthermore, we present an optimal error estimate for the scheme. In the end, several numerical experiments are presented to support our theoretical analysis.

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Data availability statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Longzhao Qi & Yanren Hou

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  1. Longzhao Qi
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Subsidized by National Natural Science Foundation of China (NSFC) (Grant No.11971378).

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Qi, L., Hou, Y. A Second Order Energy Stable BDF Numerical Scheme for the Swift–Hohenberg Equation. J Sci Comput 88, 74 (2021). https://doi.org/10.1007/s10915-021-01593-x

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