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We present a C0 interior penalty finite element method for the sixth-orderphase field crystal equation. We demonstrate that the numerical scheme isuniquely solvable, unconditionally energy stable, and convergent. We remarkthat the novelty of this paper lies in the fact that this is the first C0interior penalty finite element method developed for the phase field crystalequation. Additionally, the error analysis presented develops a detailedmethodology for analyzing time dependent problems utilizing the C0 interiorpenalty method. We furthermore benchmark our method against numericalexperiments previously established in the literature.

A C0 Interior Penalty Method for the Phase Field Crystal Equation