On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains. (Q1771835)

Poisson's equation with nonlinear boundary conditions in a boun\-ded two-dimensional domain is considered. The weak solution of this problem is approximated by means of linear triangular finite elements. Using the concept of Zlámal's ideal element, the authors examine the so-called variational crimes; namely numerical integration and approximation of a piecewise curved boundary by a polygonal one. They prove the existence and uniqueness of the discrete solution, and also the convergence of the proposed finite element method in \(H^1\)-norm without any additional regularity assumptions on the true solution.