The finite element method for nonlinear elliptic equations with discontinuous coefficients

SummaryThe 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(hε) if the exact solutionu∈H1 (Ω) is piecewise of classH1+ε (0<ε≦1);2. the convergence without any rate of convergence ifu∈H1 (Ω) only.

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