Abstract

We apply an expanded mixed finite element method, which introduces the gradient as a third explicit unknown, to solve a linear second-order elliptic equation in divergence form. Instead of using the standard dual form, we show that the corresponding variational formulation can be written as a dual-dual operator equation. We establish existence and uniqueness of solution for the continuous and discrete formulations, and provide the corresponding error analysis by using Raviart-Thomas elements. In addition, we show that the corresponding dual-dual linear system can be efficiently solved by a preconditioned minimum residual method. Some numerical results, illustrating this fact and the rate of convergence of the mixed finite element method, are also provided. © 2001 Elsevier Science B.V. All rights reserved.