Title: Mixed finite element methods for linear elasticity
with weakly imposed symmetry
Authors: Douglas N. Arnold, Richard S. Falk, and Ragnar Winther
Source: Mathematics of Computation, 76 (2007), pp. 1699-1723.
Status: Published
Abstract: In this paper, we construct new finite element methods for the
approximation of the equations of linear elasticity in three space
dimensions that produce direct approximations to both stresses and
displacements. The methods are based on a modified form of the
Hellinger--Reissner variational principle that only weakly imposes the
symmetry condition on the stresses. Although this approach has been
previously used by a number of authors, a key new ingredient here is
a constructive derivation of the elasticity complex starting
from the de~Rham complex. By mimicking this construction in the
discrete case, we derive new mixed finite elements for elasticity in a
systematic manner from known discretizations of the de Rham complex.
These elements appear to be simpler than the ones previously derived.
For example, we construct stable discretizations which use only
piecewise linear elements to approximate the stress field and piecewise
constant functions to approximate the displacement field.
Keywords: mixed method, finite element, elasticity
Subj. class.: 65N30, 74S05
URL: http://www.math.rutgers.edu/~falk/papers/mixedelas3d.pdf