Maximum angle condition in the case of some nonlinear elliptic problems.

In this paper the finite element method is analyzed for nonlinear elliptic variational problem which is formally equivalent to a two-dimensional nonlinear elliptic boundary problem with mixed nonhomogeneous boundary conditions. The given problem is analyzed under the maximum angle condition and is solved in the case of a bounded domain $\Omega$ whose boundary $\delta \Omega$ consists of two circles $\Gamma_{1}$, $\Gamma_{2}$; of the same centre $S_{0}$. These circles have the radii $R_{1}$, $R_{2} = R_{1} +\varrho$, where $\varrho \ll R_{1}$. The finite element analysis is restricted to the case of semiregular finite elements with polynomials of the first degree, At the end some numerical results are introduced.