A finite element method for Allen–Cahn equation on deforming surface

The paper studies an Allen-Cahn-type equation defined on a time-dependent surface as model of phase separation with order-disorder transition in thin material layer. By formal inner-outer expansion, it is shown that the limiting behavior solution geodesic mean curvature type flow reference coordinates. A geometrically unfitted finite element method, known trace FEM, considered for numerical equation. provides full stability analysis and convergence accounts interpolation errors approximate recovery geometry.