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

The paper is concerned with the study of the finite element solution of an elliptic equation equipped with a nonlinear Newton boundary condition. The nonlinear boundary term has a ''polynomial'' or ''quasi-polynomial'' behaviour. Special attention is paid to the effect of numerical integration for the computation of nonlinear boundary integrals. The solvability of the discrete problem and the convergence of the approximate solutions to the exact solution are discussed.