CSAR Noon Seminar
Jonathan Shewchuk,
University of California at Berkeley
DATE: Wednesday, September 24, 2003
TIME: 12:00 Noon
PLACE: 2240 DCL
1304 W. Springfield Ave., Urbana, IL
TITLE: What is a Good Linear Finite Element?
Interpolation, Conditioning, Anisotropy, and Quality Measures
ABSTRACT
I present new bounds on interpolation errors over linear triangular and
tetrahedral elements, including bounds for cases where the function
being interpolated has anisotropic curvature. I also discuss the
relationship between element shape and stiffness matrix conditioning,
for isotropic and anisotropic PDEs. From these relationships I develop
element quality measures suitable for use in numerical or combinatorial
optimization of meshes, to help reduce the interpolation error or
condition number. Some surprising conclusions about anisotropy (and
the large angle condition) follow from these results.