On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains

summary:The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition considered in a two-dimensional nonpolygonal domain with a curved boundary. The existence and uniqueness of the solution of the continuous problem is a consequence of the monotone operator theory. The main attention is paid to the effect of the basic finite element variational crimes: approximation of the curved boundary by a polygonal one and the evaluation of integrals by numerical quadratures. With the aid of some important properties of Zlámal’s ideal triangulation and interpolation, the convergence of the method is analyzed