The paper studies a scalar auxiliary variable (SAV) method to solve the Cahn-Hilliard equation with degenerate mobility posed on a smooth closed surface {\Gamma}. The SAV formulation is combined with adaptive time stepping and a geometrically unfitted trace finite element method (TraceFEM), which embeds {\Gamma} in R3. The stability is proven to hold in an appropriate sense for both first- and second-order in time variants of the method. The performance of our SAV method is illustrated through a series of numerical experiments, which include systematic comparison with a stabilized semi-explicit method.

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