A scalar auxiliary variable unfitted FEM for the surface Cahn-Hilliard equation

06/01/2023

∙

by   Maxim Olshanskii, et al.

∙

0

∙

share

The paper studies a scalar auxiliary variable (SAV) method to solve the Cahn-Hilliard equation with degenerate mobility posed on a smooth closed surface Γ. The SAV formulation is combined with adaptive time stepping and a geometrically unfitted trace finite element method (TraceFEM), which embeds Γ 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.