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Unconditionally stable schemes for equations of thin film epitaxy

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  • We present unconditionally stable and convergent numerical sche- mes for gradient flows with energy of the form $ \int_\Omega( F(\nabla\phi(\x)) + \frac{\epsilon^2}{2}|\Delta\phi(\x)|^2 )$dx. The construction of the schemes involves an appropriate extension of Eyre's idea of convex-concave decomposition of the energy functional. As an application, we derive unconditionally stable and convergent schemes for epitaxial film growth models with slope selection (F(y)= 1/4(|y|2-1)2) and without slope selection (F(y)= -1/2ln(1+|y|2)). We conclude the paper with some preliminary computations that employ the proposed schemes.
    Mathematics Subject Classification: Primary: 65M12; Secondary: 37L65.


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