A mixed finite element method for a strongly nonlinear second-order elliptic problem

Abstract

The approximation of the solution of the first boundary value problem for a strongly nonlinear second-order elliptic problem in divergence form by the mixed finite element method is considered. Existence and uniqueness of the approximation are proved and optimal error estimates in L 2 {L^2} are established for both the scalar and vector functions approximated by the method. Error estimates are also derived in L q , 2 ≤ q ≤ + ∞ {L^q},2 \leq q \leq + \infty .