Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation

• Published in: Advances in computational mathematics Vol. 46; no. 3
• Main Authors: Li, Xiaoli, Shen, Jie
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2020; Springer Nature B.V
• Subjects: Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Robustness (mathematics); Spectra; Spectral methods; Stability; Visualization; 65M15; Phase field crystal; Error estimates; Scalar auxiliary variable (SAV); 65M70; Energy stability; Fourier-spectral method; 65M12; 35G25

We consider fully discrete schemes based on the scalar auxiliary variable (SAV) approach and stabilized SAV approach in time and the Fourier-spectral method in space for the phase field crystal (PFC) equation. Unconditionally, energy stability is established for both first- and second-order fully di...