Title:         Remarks on mixed finite element methods
               for problems with rough coefficients

Authors:       Richard S. Falk and John E. Osborn

Source:        Math. Comp, 62 (1994)

Status:        Published

Abstract:      This paper considers the finite element
approximation of elliptic boundary value problems in
divergence form with rough coefficients. The solution of
such problems will, in general, be rough, and it is
well-known that the usual (Ritz or displacement) finite
element method will be inaccurate in general.  The
purpose of the paper is to help clarify the issue of
whether the use of mixed variational principles leads to
finite element schemes, i.e., to mixed methods, that are
more accurate than the Ritz or displacement method for
such problems.  For one dimensional problems, it is
well-known that certain mixed methods are more accurate
and robust than the Ritz method for problems with rough
coefficients.  Our results for two dimensional problems
are mostly of a negative character.  Through an examination
of examples, we show that certain standard mixed methods fail
to provide accurate approximations for problems with rough
coefficients except in some special situations.

Keywords:      finite elements, mixed methods

Subj. class.:  65N30