Summary
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 convergenceO(h ε) if the exact solutionu∈H 1 (Ω) is piecewise of classH 1+ε (0<ε≦1);2. the convergence without any rate of convergence ifu∈H 1 (Ω) only.
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