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.
Original language | English |
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Pages (from-to) | 653-674 |
Number of pages | 22 |
Journal | Mathematics of Computation |
Volume | 84 |
Issue number | 292 |
DOIs | |
Publication status | Published - 1 Jan 2014 |
Keywords
- Convergence
- Energy decay
- Finite difference scheme
- Linearized difference scheme
- Molecular beam epitaxy
- Stability
ASJC Scopus subject areas
- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics