A C0 interior penalty method for the phase field crystal equation. Issue 3 (30th December 2022)

• Record Type: Journal Article
• Authors: Diegel, Amanda E.; Sharma, Natasha S.
• Is Part Of: Numerical methods for partial differential equations. Volume 39:Issue 3(2023)
• Page Start: 2510
• Page End: 2537
• Publication Date: 2022-12-30
• Subjects: C0 interior penalty method -- energy stability -- finite element method -- higher‐order methods -- nonlinear partial differential equation -- phase field crystal -- sixth‐order parabolic; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22976
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: We present a C 0 interior penalty finite element method for the sixth‐order phase field crystal equation. We demonstrate that the numerical scheme is uniquely solvable, unconditionally energy stable, and convergent. We remark that the novelty of this paper lies in the fact that this is the first C 0 interior penalty finite element method developed for the phase field crystal equation. Additionally, the error analysis presented develops a detailed methodology for analyzing time dependent problems utilizing the C 0 interior penalty method. We furthermore benchmark our method against numerical experiments previously established in the literature.