TY - JOUR
T1 - Generalized SAV approaches for gradient systems
AU - Cheng, Qing
AU - Liu, Chun
AU - Shen, Jie
N1 - Publisher Copyright:
© 2021
PY - 2021/10/1
Y1 - 2021/10/1
N2 - We propose in this paper three generalized auxiliary scalar variable (G-SAV) approaches for developing, efficient energy stable numerical schemes for gradient systems. The first two G-SAV approaches allow a range of functions in the definition of the SAV variable, furthermore, the second G-SAV approach only requires the total free energy to be bounded from below as opposed to the requirement that the nonlinear part of the free energy to be bounded from below. On the other hand, the third G-SAV approach is unconditionally energy stable with respect to the original free energy as opposed to a modified energy. Ample numerical results for various gradient systems are presented to validate the effectiveness and accuracy of the proposed G-SAV approaches.
AB - We propose in this paper three generalized auxiliary scalar variable (G-SAV) approaches for developing, efficient energy stable numerical schemes for gradient systems. The first two G-SAV approaches allow a range of functions in the definition of the SAV variable, furthermore, the second G-SAV approach only requires the total free energy to be bounded from below as opposed to the requirement that the nonlinear part of the free energy to be bounded from below. On the other hand, the third G-SAV approach is unconditionally energy stable with respect to the original free energy as opposed to a modified energy. Ample numerical results for various gradient systems are presented to validate the effectiveness and accuracy of the proposed G-SAV approaches.
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U2 - 10.1016/j.cam.2021.113532
DO - 10.1016/j.cam.2021.113532
M3 - Article
AN - SCOPUS:85102786649
SN - 0377-0427
VL - 394
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
M1 - 113532
ER -