CSAR Noon Seminar
Fatih Celiker
University of Minnesota
DATE: Wednesday, March 16, 2005
TIME: 12:00 Noon
PLACE: 2240 DCL
TITLE: Locking-Free Optimal Discontinuous Galerkin Methods for
Timoshenko Beams
ABSTRACT
In this talk, we study discontinuous Galerkin (DG) methods for
Timoshenko beams. It is well-known that when the thickness of the beam
is small, the classical continuous finite element method suffers from
so-called shear-locking if suitable modifications are not made. We
show that a wide family of DG methods are free from locking, and they
converge to the exact solution at an optimal rate. We also uncover and
study new superconvergence properties of numerical traces at the mesh
nodes of quantities that approximate those of interest in the
solution. We prove that they converge with order 2p+1 if polynomials
of degree p are employed to approximate all the unknowns. As a simple
consequence of this superconvergence property, we define a new
element-by-element post-processing of the DG approximation that
converges uniformly with order 2p+1 in the entire domain, rather than
merely at the nodes of the mesh, which is a significant improvement in
the rate of convergence. Due to the local nature of the
post-processing, its computational cost is negligible compared with
that of computing the original DG solution.