A benchmark for the surface Cahn-Hilliard equation

We study the surface Cahn-Hilliard equation, an often used model for spinodal decomposition and coarsening effects on surfaces. As the width of the diffuse interface shrinks to zero one expects a convergence towards a surface Hele-Shaw model. While results from formal matched asymptotic expansions confirm this conjecture, a numerical reproduction of this asymptotic behavior has not been provided, yet. It is the purpose of this contribution, to fill this gap and present a rotationally symmetric example on the standard sphere, where analytic expressions for the surface Hele-Shaw model allow a comparison with numerical results for the surface Cahn-Hilliard equation. (C) 2015 Elsevier Ltd. All rights reserved.