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Full-Text Articles in Physical Sciences and Mathematics
A Linear Energy Stable Scheme For A Thin Film Model Without Slope Selection, Wenbin Chen, Sidafa Conde, Cheng Wang, Xiaoming Wang, Steven M. Wise
A Linear Energy Stable Scheme For A Thin Film Model Without Slope Selection, Wenbin Chen, Sidafa Conde, Cheng Wang, Xiaoming Wang, Steven M. Wise
Mathematics and Statistics Faculty Research & Creative Works
We present a linear numerical scheme for a model of epitaxial thin film growth without slope selection. the PDE, which is a nonlinear, fourth-order parabolic equation, is the L2 gradient flow of the energy ∫Ω(-1/2 ln(1 + |ø|2) + ε2 2 |Ø(x)|2) dx. the idea of convex-concave decomposition of the energy functional is applied, which results in a numerical scheme that is unconditionally energy stable, i.e., energy dissipative. the particular decomposition used here places the nonlinear term in the concave part of the energy, in contrast to a previous convexity splitting scheme. as a result, the numerical scheme is fully …