Event Detail

Event Type: 
Department Colloquium
Date/Time: 
Monday, January 13, 2014 - 08:00
Location: 
Kidd 350

Speaker Info

Institution: 
Portland State, Fariborz Maseeh Department of Mathematics and Statistics
Abstract: 

Error estimation and adaptive approximation are essential
components of high-performance finite element computations. In this
talk we consider both boundary value problems (BVPs) and eigenvalue
problems (EPs) for a Schr\"odinger operator with inverse-square
potential, $-\Delta +c^2 r^{-2} $. The inverse-square potential
$c^2 r^{-2}$ not only gives rise to new sources of singularities
in the solution of BVPs and EPs when $c>0$ (the case $c=0$
is the familiar Laplacian), but also requires a different approach to both
analysis and numerical analysis. We will discuss an effective means
of estimating errors in finite element discretizations, and
demonstrate how one might use them to adaptively improve
approximations in an efficient way. Analysis is carried out on
families of triangulations which are geometrically graded based on a
priori
knowledge of worst case singularities (which are possible for the
model problem), and empirical comparisons are made between this a
priori
approach and families of triangulations which are adaptively refined
using local error indicators.