Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/67393
Title: Convergence of a fast explicit operator splitting method for the epitaxial growth model with slope selection
Authors: Li, X
Qiao, ZH 
Zhang, H
Keywords: Epitaxial growth
Fast explicit operator splitting
Finite difference method
Pseudo spectral method
Stability
Convergence
Issue Date: 2017
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on numerical analysis, 2017, v. 55, no. 1, p. 265-285 How to cite?
Journal: SIAM journal on numerical analysis 
Abstract: A fast explicit operator splitting method for the epitaxial growth model with slope selection has been presented in [Cheng et al., T. Comput. Phys., 303 (2015), pp. 45-65]. The original problem is split into linear and nonlinear subproblems. For the linear part, the pseudospectral method is adopted; for the nonlinear part, a 33-point difference scheme is constructed. Here, we give a compact center-difference scheme involving fewer points for the nonlinear subproblem. In addition, we analyze the convergence rate of the algorithm. The global error order O(T-2 + h(4)) in discrete L-2-norm is proved theoretically and verified numerically. Some numerical experiments show the robustness of the algorithm for small coefficients of the fourth-order term for the one-dimensional case. In addition, coarsening dynamics are simulated in large domains and the 1/3 power laws are observed for the two-dimensional case.
URI: http://hdl.handle.net/10397/67393
ISSN: 0036-1429
EISSN: 1095-7170
DOI: 10.1137/15M1041122
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