2,451 research outputs found
Mixed finite element methods for linear elasticity with weakly imposed symmetry
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.Comment: to appear in Mathematics of Computatio
Why Judges Don\u27t Like Petitions for Rehearing
Petitions for en banc rehearings are rarely granted. A Senior Judge for the United States Court of Appeals for the Eighth Circuit provides a history and reasoning of the rehearing process and his personal observations on those petitions and processes in today\u27s court
Unpublished Opinions: A Comment
The Honorable Richard S. Arnold gives a federal appellate judge’s perspective of the unpublished opinions debate
- …