The authors consider the approximation of the solution of strongly nonlinear two-dimensional second-order elliptic boundary value problems in divergence form by using the mixed finite element method. The spatial domain is considered to be a bounded, convex domain with - boundary. Furthermore, the coefficient vector is assumed to have a bounded positive definite Jacobian with respect to the second argument. This assumption implies that the gradient of the solution can be locally represented as a function of the “flux”. The authors assume that such a representation is global.
Theorems for the existence and uniqueness of the approximation are proved making use of the Raviart-Thomas space of index and introducing and Raviart-Thomas projections. After that, the authors extend some previous results of F. A. Milner [Math. Comput. 44, 303-320 (1985; Zbl 0567.65079)] and derive error estimates in , using some generalizations of the lemmas (proved in the previous paragraph) and Nitsche’s weighted -norms.