MIXED FINITE-ELEMENT METHODS FOR ELLIPTIC PROBLEMS

This paper treats the basic ideas of mixed finite element methods at an introductory level. Although the viewpoint presented is that of a mathematician, the paper is aimed at practitioners and the mathematical prerequisites are kept to a minimum. A classification of variational principles and of the corresponding weak formulations and Galerkin methods-displacement, equilibrium and mixed-is given and illustrated through four significant examples. The advantages and disadvantages of mixed methods are discussed. The concepts of convergence, approximability and stability and their interrelations are developed, and a résumé is given of the stability theory which governs the performance of mixed methods. The paper concludes with a survey of techniques that have been developed for the construction of stable mixed methods and numerous examples of such methods. © 1990.