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- W3021016296 abstract "In this paper we investigate the long time stability of the implicit Euler scheme for the Cahn-Hilliard equation with polynomial nonlinearity. The uniform estimates in H−1 and Hαs (s=1,2,3) spaces independent of time discrete step-sizes are derived for the numerical solution produced by this classical scheme with variable time step-sizes. The uniform Hα3 bound is obtained on basis of the uniform H1 estimate for the discrete chemical potential which is derived with the aid of the uniform discrete Gronwall lemma. A comparison with the estimates for the continuous-in-time dynamical system reveals that the classical implicit Euler method can completely preserve the long time behaviour of the underlying system. Such a long time behaviour is also demonstrated by the numerical experiments with the help of Fourier pseudospectral space approximation." @default.
- W3021016296 created "2020-05-13" @default.
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- W3021016296 date "2021-07-01" @default.
- W3021016296 modified "2023-09-24" @default.
- W3021016296 title "Long time <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.svg><mml:msubsup><mml:mrow><mml:mi mathvariant=script>H</mml:mi></mml:mrow><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msubsup></mml:math> stability of a classical scheme for Cahn-Hilliard equation with polynomial nonlinearity" @default.
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- W3021016296 doi "https://doi.org/10.1016/j.apnum.2021.02.005" @default.
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