Numeerisen analyysin ja laskennallisen
tieteen seminaari
3.10.2005 klo
14.15
U356
Lourenco Beirao da Veiga and Jarkko Niiranen
A family of C^0
elements for Kirchhoff plates
A new family of finite elements for the bending problem of
Kirchhoff plates is introduced. The presented method has the advantage
of
requiring only a $C^0$ global regularity condition on the deflections,
therefore allowing also a low order polynomial degree. When a
Kirchhoff plate bending problem is interpreted as a "zero
thickness" limit of a Reissner-Mindlin problem, an additional
inconsistency
arises in the presence of free boundary conditions.
In the finite element method presented, this inconsistency is avoided
adding
certain natural terms to the discrete bilinear form of the problem,
leading to
an optimally convergent method.
During the talk, both a-priori and an a-posteriori error
estimates are shown. In particular, the local a-posteriori error
estimator obtained is proven to be both reliable and efficient.
Finally, we present some numerical tests which show on one hand
the optimal rate of convergence of the proposed finite elements,
and on the other hand the slow $O(h^{1/2})$ convergence of the
original "Reissner-Mindlin limit" method.