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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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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DOI: https://doi.org/10.1007/s10915-021-01593-x