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On the worst scenario method: application to a quasilinear elliptic 2D-problem with uncertain coefficients. (English) Zbl 1249.35043
In this paper the author extends his earlier results to a quasilinear elliptic 2D-problem with uncertain coefficients. The existence of the worst scenario is proved through of the convergence of a sequence of approximate worst scenario. Furthermore, it is shown that the Galerkin approximation of the state solution can be calculated by means of the Kachanov method as a limit of a sequence of solutions to linearized problems.

MSC:
35D30 Weak solutions to PDEs
35G30 Boundary value problems for nonlinear higher-order PDEs
47H05 Monotone operators and generalizations
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:
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