Event Type:

Department Colloquium

Date/Time:

Monday, January 13, 2014 - 08:00

Location:

Kidd 350

Guest Speaker:

Jeffrey Ovall

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

priori

using local error indicators.