Abstract

We apply a mixed finite element method to solve a nonlinear second order elliptic equation in divergence form with mixed boundary conditions. Our approach introduces the trace of the solution on the Neumann boundary as a further unknown that acts also as a Lagrange multiplier. We show that the resulting variational formulation and an associated discrete scheme defined with Raviart-Thomas spaces are well posed, and derive the usual a priori estimates and the corresponding rate of convergence. In addition, we develop a Bank-Weiser type a posteriori error analysis and provide an implicit reliable and quasi-efficient estimate, and a fully explicit reliable one. Several numerical results illustrate the suitability of the explicit a posteriori estimate for the adaptive computation of the discrete solutions. © 2003 IMACS. Published by Elsevier B.V. All rights reserved.