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Title: Convergence of a fast explicit operator splitting method for the epitaxial growth model with slope selection
Authors: Li, X 
Qiao, ZH 
Zhang, H
Issue Date: 2017
Source: SIAM journal on numerical analysis, 2017, v. 55, no. 1, p. 265-285
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.
Keywords: Epitaxial growth
Fast explicit operator splitting
Finite difference method
Pseudo spectral method
Stability
Convergence
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM journal on numerical analysis 
ISSN: 0036-1429
EISSN: 1095-7170
DOI: 10.1137/15M1041122
Rights: © 2017 Society for Industrial and Applied Mathematics
Posted with permission of the publisher.
The following publication Li, X., Qiao, Z., & Zhang, H. (2017). Convergence of a Fast Explicit Operator Splitting Method for the Epitaxial Growth Model with Slope Selection. SIAM Journal on Numerical Analysis, 55(1), 265-285 is available at https://doi.org/10.1137/15M1041122.
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