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Title: Stability and convergence of second-order schemes for the nonlinear epitaxial growth model without slope selection
Authors: Qiao, Z 
Sun, ZZ
Zhang, Z
Keywords: Convergence
Energy decay
Finite difference scheme
Linearized difference scheme
Molecular beam epitaxy
Issue Date: 2014
Publisher: American Mathematical Society
Source: Mathematics of computation, 2014, v. 84, no. 292, p. 653-674 How to cite?
Journal: Mathematics of computation 
Abstract: We present one nonlinear and one linearized numerical schemes for the nonlinear epitaxial growth model without slope selection. Both schemes are proved to be uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. By introducing an auxiliary variable in the discrete energy functional, the energy stability of both schemes is guaranteed regardless of the time step size, in the sense that a modified energy is monotonically nonincreasing in discrete time. Numerical experiments are carried out to support the theoretical claims.
ISSN: 0025-5718
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