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.

翻译：本文研究了一种用于求解光滑闭曲面{\Gamma}上具有退化迁移率的Cahn-Hilliard方程的标量辅助变量（SAV）方法。该SAV格式结合了自适应时间步长与几何无拟合追踪有限元法（TraceFEM），其中曲面{\Gamma}嵌入于三维欧氏空间R3中。证明了该方法在时间上的一阶与二阶变体均具有适当意义上的稳定性。通过一系列数值实验验证了我们所提出SAV方法的性能，其中包括与一种稳定化半隐式方法的系统比较。