A linearly second-order, unconditionally energy stable scheme and its error estimates for the modified phase field crystal equation. (1st December 2021)

• Record Type: Journal Article
• Authors: Pei, Shuaichao; Hou, Yanren; Li, Qi
• Is Part Of: Computers & mathematics with applications. Volume 103(2021)
• Page Start: 104
• Page End: 126
• Publication Date: 2021-12-01
• Subjects: Modified phase field equation -- Unconditional energy stability -- Error estimates; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.10.029
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We carry out error estimates for a linear, second-order, unconditionally energy stable, semi-discrete time stepping scheme, which is based on the Lagrange Multiplier approach and could also be viewed as a special case of the invariant energy quadratization approach, for the modified phase field crystal equation. At each time step, the proposed scheme only requires solving several linear equations. Rigorous proofs are presented to demonstrate the unique solvability, mass conservation, and unconditional energy stability of the scheme. Various numerical experiments in 2D and 3D are performed to validate the accuracy, unconditional energy stability and mass conservation of the proposed numerical strategy.