A C0 Interior Penalty Method for the Phase Field Crystal Equation

2020/11/17 by Amanda E. Diegel, Diegel, Amanda E., N. Sharma +1 · 1 citation
Materials Science · Mathematics · #65M60 #Differential Equations and Numerical Methods #FOS: Mathematics #G.1.8 #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2011.08937

openalex publication_date 2020/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a C0 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 C0 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 C0 interior penalty method. We furthermore benchmark our method against numerical experiments previously established in the literature.

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• An Immersed C⁰ Interior Penalty Method for Biharmonic Interface Problems

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