Finite element approximation of a problem with a nonlinear Newton boundary condition

The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition. The existence and uniqueness of the solution of the continuous problem is established with the aid of the monotone operator theory, The main attention is paid to the investigation of the finite element approximation using numerical integration for the computation of nonlinear boundary integrals. The solvability of the discrete finite element problem is proved and the convergence of the approximate solutions to the exact one is analysed.