Abstract
We present unconditionally stable and convergent numerical schemes for gradient flows with energy of the form integral(Omega)(F(del phi(x)) + is an element of(2)/2 vertical bar del phi(x)vertical bar) 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 slopes election (F(y) = 1/4(vertical bar y vertical bar(2) - 1)(2)) and without slope selection (F(y) = -1/2ln(1 + vertical bar y vertical bar(2))). We conclude the paper with some preliminary computations that employ the proposed schemes.