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We consider formal matched asymptotics to show the convergence of adegenerate area preserving surface Allen-Cahn equation to its sharp interfacelimit of area preserving geodesic curvature flow. The degeneracy results from asurface de Gennes-Cahn-Hilliard energy and turns out to be essential tonumerically resolve the dependency of the solution on geometric properties ofthe surface. We experimentally demonstrate convergence of the numericalalgorithm, which considers a graph formulation, adaptive finite elements and asemi-implicit discretization in time, and uses numerical solutions of the sharpinterface limit, also considered in a graph formulation, as benchmarksolutions.

Degenerate area preserving surface Allen-Cahn equation and its sharp interface limit