THE FINITE-ELEMENT METHOD FOR NONLINEAR ELLIPTIC-EQUATIONS WITH DISCONTINUOUS COEFFICIENTS

The study of the finite element approximation to nonlinear second order elliptic boundary value problems with discontinuous coefficients is presented in the case of mixed Dirichlet-Neumann boundary conditions. The change in domain and numerical integration are taken into account. With the assumptions which guarantee that the corresponding operator is strongly monotone and Lipschitz-continuous the following convergence results are proved: 1. the rate of convergence O(hε) if the exact solution u∈H1 (Ω) is piecewise of class H1+ε (0<ε≦1);2. the convergence without any rate of convergence if u∈H1 (Ω) only. © 1990 Springer-Verlag.