Approximation of the capillarity problem by an augmented Lagrangian method

We propose an algorithm to compute an approximation of capillary surfaces in a gravitational field. This algorithm is based on a decomposition-coordination method by augmented lagrangians and the discretization is done using the finite element method. We study the convergence of the algorithm and the error of discretization for the axisymmetric case; some numerical results are given. This method can be generalized to a two-dimensional space.