Unconditionally stable schemes for equations of thin film epitaxy

Abstract

We present unconditionally stable and convergent numerical schemes for gradient flows with energy of the form √ (F(Δφ(x)) +ε2/2|Δ(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) = - 1/21n(1 + |y|2 )). We conclude the paper with some preliminary computations that employ the proposed schemes.