Numerical behavior of a linear mixed kinetic-diffusion model for surfactant adsorption at the air-water interface

This paper concerns the numerical behavior of the solution to a problem including a linear mixed kinetic-diffusion model for surfactant adsorption at the air-water interface. The existence and uniqueness of a weak solution is recalled. Then, fully discrete approximations are obtained by using a finite element method and the backward Euler scheme. Error estimates are stated from which, under adequate additional regularity conditions, the linear convergence of the algorithm is deduced. Finally, several numerical simulations are presented in order to demonstrate the behavior of the solution for commercially available surfactants.