期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 51, 期 5, 页码 2851-2873出版社
SIAM PUBLICATIONS
DOI: 10.1137/120880677
关键词
phase field crystal; modified phase field crystal; pseudoenergy; convex splitting; energy stability; second order convergence
资金
- NSF-DMS [1115420]
- NSF-DCNS [0959382, AFOSR-10418149]
- NSFC [11271281]
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1105409] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1115420, 1115390] Funding Source: National Science Foundation
In this paper we provide a detailed convergence analysis for an unconditionally energy stable, second order accurate convex splitting scheme for the modified phase field crystal equation, a generalized damped wave equation for which the usual phase field crystal equation is a special degenerate case. The fully discrete, fully second order finite difference scheme in question was derived in a recent work [A. Baskaran et al., J. Comput. Phys., 250 (2013), pp. 270-292]. An introduction of a new variable psi, corresponding to the temporal derivative of the phase variable phi, could bring an accuracy reduction in the formal consistency estimate, because of the hyperbolic nature of the equation. A higher order consistency analysis by an asymptotic expansion is performed to overcome this difficulty. In turn, second order convergence in both time and space is established in a discrete L-infinity(0, T; H-3) norm.
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