On minimization of one integral functional by the Ritz method - Minenko, A. S. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
Using the variational method, we investigate a nonlinear problem with a Bernoulli condition in the form of an inequality on a free boundary. We prove a solvability theorem and establish the convergence of an approximate solution obtained by the Ritz method to the exact solution in certain metrics.