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A mixed finite element method for a nonlinear Dirichlet problem. (English) Zbl 0909.65086

The author studies a mixed finite element method for a nonlinear Dirichlet problem in both two and three dimensions. Existence and uniqueness results are given for the continuous problem and its approximation. An error bound is proved. The results received may be considered as an important step towards the treatment of Ladyzhenskaya flows or quasi-Newtonian flows obeying the power law.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
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