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Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model. (English) Zbl 1380.65209
Summary: In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first-order Euler method, the second-order backward differentiation formulas (BDF2) and the second-order Crank-Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposed schemes.

MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
82D25 Statistical mechanical studies of crystals
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