A Scalar Auxiliary Variable(SAV) Finite Element Numerical Scheme For The Cahn-Hilliard-Hele-Shaw System With Dynamic Boundary Conditions

In this paper,the Cahn-Hilliard-Hele-Shaw(CHHS)system is considered with the dynamic boundary conditions.By introducing a surface free energy functional,combined with the bulk free energy functional,we give the corresponding specific equations.Once the phase field model is obtained,the solution becomes a crucial issue.In this paper,we adopt the combination of scalar auxiliary variable(SAV)method and finite element spatial approximation for the system.The finite element method is very suitable for dealing with problems with dynamic boundary conditions for its unique advantages,the SAV method only needs to introduce auxiliary variables that do not depend on space,and are able to make the modified energy satisfy energy dissipation law,which is also proved in the paper.Subsequently,a fully discrete SAV finite element scheme is proposed,with the energy dissipation laws established at a theoretical level.In addition,the convergence analysis is provided for the proposed SAV numerical scheme.