Error estimates for the finite element solution of elliptic problems with nonlinear Newton boundary conditions

摘要

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 a consequence of the monotone operator theory. The main attention is paid to the investigation of the finite element approximation using numerical integration for the evaluation of boundary integrals. The error estimates for the solution of the discrete finite element problem are derived.