A Posteriori error estimates for the mixed finite element method with lagrange multipliers

We consider the mixed finite element method with Lagrange multipliers as applied to second-order elliptic equations in divergence form with mixed boundary conditions. The corresponding Galerkin scheme is defined by using Raviart-Thomas spaces. We develop a posteriori error analyses yielding a reliable and efficient estimate based on residuals, and a reliable and quasi-efficient estimate based on local problems, respectively. Several numerical results illustrate the suitability of these a posteriori estimates for the adaptive computation of the discrete solutions. (c) 2004 Wiley Periodicals, Inc.