Title:         Mixed finite element methods for elliptic problems

Authors:       Douglas N. Arnold

Source:        Comput. Methods Appl. Mech. Engrg. 82 (1990), pp. 281-300

Status:        Published

Abstract:  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 resume 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.

Keywords:      mixed method, finite element, variational principle

Subj. class.:  65N30, 73C35, 73K25

URL:           http://ima.umn.edu/~arnold/papers/mixed.pdf