Numerical analysis of an adsorption dynamic model at the air-water interface

- An adsorption dynamic model for surfactants is numerically studied.
- A priori error estimates are proved by using Gronwall's inequality.
- Linear convergence is obtained using regularity and an interpolation operator.
- Numerical results show the accuracy and the peformance of the approximations.

In this paper we deal with the numerical analysis of an adsorption dynamic model arising in a surfactant solution at the air-water interface; the diffusion model is considered together with the so-called Langmuir isotherm. An existence and uniqueness result is stated. Then, fully discrete approximations are introduced by using a finite element method and a hybrid combination of backward and forward Euler schemes. Error estimates are proved from which, under adequate additional regularity conditions, the linear convergence of the algorithm is derived assuming a dependence between both spatial and time discretization parameters. Finally, some numerical simulations are presented in order to demonstrate the accuracy of the algorithm and the behaviour of the solution for two commercially available surfactants.