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MATHEMATICS OF COMPUTATION Volume 76, Number 260, October 2007, Pages 16991723
 

Summary: MATHEMATICS OF COMPUTATION
Volume 76, Number 260, October 2007, Pages 1699­1723
S 0025-5718(07)01998-9
Article electronically published on May 9, 2007
MIXED FINITE ELEMENT METHODS FOR LINEAR
ELASTICITY WITH WEAKLY IMPOSED SYMMETRY
DOUGLAS N. ARNOLD, RICHARD S. FALK, AND RAGNAR WINTHER
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 Hellinger­Reissner 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 com-
plex starting from the de Rham complex. By mimicking this construction in
the discrete case, we derive new mixed finite elements for elasticity in a sys-
tematic 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

  

Source: Arnold, Douglas N. - School of Mathematics, University of Minnesota

 

Collections: Mathematics