Quasi-optimal meshes in three dimensions
Victor Nistor
Department of Mathematics
The Pennsylvania State University
University Park, PA 16802
Abstract
The finite element solution of elliptic problems leads to large systems of equations. The
time required to solve these systems grows with the number of unknowns. It is desirable
then to find finite dimensional spaces Sn that posses good approximation properties, so that
a good approximation un ∈ Sn of the solution is obtained with the dimension of Sn small.
(The dimension of the Finite Element Space Sn is the same as the dimension of the resulting
system.) I will first recall for the benefit of the students the main definitions and results
pertaining to the finite element method. Then I will show how to construct sequences Sn
that have (quasi-)optimal approximation properties first in two and then in three dimensions.
Some of these results are new and were obtained in joint works with C. Bacuta, H. Li, A.
Mazzucato, and L. Zikatanov. The talk will be accessible also to non-mathematicians with
an interest in numerical methods.
Converted from 2006-9-15.pdf (PDF).