A generalized SAV approach with relaxation for dissipative systems
نویسندگان
چکیده
The scalar auxiliary variable (SAV) approach \cite{shen2018scalar} and its generalized version GSAV proposed in \cite{huang2020highly} are very popular methods to construct efficient accurate energy stable schemes for nonlinear dissipative systems. However, the discrete value of SAV is not directly linked free system, may lead inaccurate solutions if time step sufficiently small. Inspired by relaxed method \cite{jiang2022improving} gradient flows, we propose this paper a with relaxation (R-GSAV) general R-GSAV preserves all advantages appraoch, addition, it dissipates modified that original energy. We prove $k$-th order implicit-explicit (IMEX) based on unconditionally stable, carry out rigorous error analysis $k=1,2,3,4,5$. present ample numerical results demonstrate improved accuracy effectiveness approach.
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2022
ISSN: ['1090-2716', '0021-9991']
DOI: https://doi.org/10.1016/j.jcp.2022.111311