Efficient Fully Discrete Finite-Element Numerical Scheme with Second-Order Temporal Accuracy for the Phase-Field Crystal Model

Jun Zhang and Xiaofeng Yang
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Jun Zhang: Guizhou Key Laboratory of Big Data Statistical Analysis, Guizhou University of Finance and Economics, Guiyang 550025, China
Xiaofeng Yang: Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA

Mathematics, 2022, vol. 10, issue 1, 1-11

Abstract: In this paper, we consider numerical approximations of the Cahn–Hilliard type phase-field crystal model and construct a fully discrete finite element scheme for it. The scheme is the combination of the finite element method for spatial discretization and an invariant energy quadratization method for time marching. It is not only linear and second-order time-accurate, but also unconditionally energy-stable. We prove the unconditional energy stability rigorously and further carry out various numerical examples to demonstrate the stability and the accuracy of the developed scheme numerically.

Keywords: phase-field crystal; IEQ; decoupled; linear; Cahn–Hilliard; unconditional energy stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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