This paper presents a mixed finite element method for solving second-order elliptic problems. The method is based on the Hellinger-Reissner variational principle, which allows the elimination of constraints by introducing a Lagrange multiplier. The method is particularly useful for practical problems and has been applied to nonlinear radiative transfer problems. The paper discusses the derivation of the mixed variational formulation of the problem and defines the related discrete elements. It also presents an error analysis of the associated finite element method and generalizes the results to mixed methods using rectangular elements. The paper references several key works in the field of mixed methods, including those by Brezzi & Raviart, Ciarlet & Raviart, Johnson, and Miyoshi. The paper also introduces notation for Sobolev spaces and their norms, which are essential for the analysis of the finite element method. The method is designed to handle the equilibrium equation by constructing a finite-dimensional submanifold of the solution space and finding the minimizer of the complementary energy functional over this submanifold. The use of mixed methods allows for more accurate solutions to elliptic problems, particularly when the solution has a high gradient or when the problem is ill-conditioned. The paper concludes with an outline of the structure of the paper, including the derivation of the mixed variational formulation, the error analysis, and the generalization of the results to rectangular elements.This paper presents a mixed finite element method for solving second-order elliptic problems. The method is based on the Hellinger-Reissner variational principle, which allows the elimination of constraints by introducing a Lagrange multiplier. The method is particularly useful for practical problems and has been applied to nonlinear radiative transfer problems. The paper discusses the derivation of the mixed variational formulation of the problem and defines the related discrete elements. It also presents an error analysis of the associated finite element method and generalizes the results to mixed methods using rectangular elements. The paper references several key works in the field of mixed methods, including those by Brezzi & Raviart, Ciarlet & Raviart, Johnson, and Miyoshi. The paper also introduces notation for Sobolev spaces and their norms, which are essential for the analysis of the finite element method. The method is designed to handle the equilibrium equation by constructing a finite-dimensional submanifold of the solution space and finding the minimizer of the complementary energy functional over this submanifold. The use of mixed methods allows for more accurate solutions to elliptic problems, particularly when the solution has a high gradient or when the problem is ill-conditioned. The paper concludes with an outline of the structure of the paper, including the derivation of the mixed variational formulation, the error analysis, and the generalization of the results to rectangular elements.