## Research

### What is numerical analysis? [Click here for a non-technical explanation]

My research field is numerical analysis , specifically, the numerical analysis of partial differential equations. I am also interested in finding new ways to promote mathematics in adult and K-12 populations, and intersections between mathematics and the humanities. (See Outreach Activities for more on this.)

- Finite element methods for elliptic problems, in particular the p version and hp version.

What are finite elements? [Click here for a non-technical explanation] - Numerical approximation of thin domains such as plates and shells.
- Computational analysis of woven composite materials

### Research on Buckling

The above picture shows the first three buckling modes of a stiffened plate. In the first two, the whole plate buckles, together with the stiffener (which is the thin strip on the underside). In the third, no buckling appears to take place, since the plate acts as a clamp (as if the stiffener was clamped into a wall, for instance). The buckling now only takes place in the stiffener instead (see detail), a phenomenon known as `crippling.' The above computations were done on the commercial engineering code Stress Check (ESRD, St. Louis).

Using the finite element code STRESS CHECK with Prof. Ricardo Actis at the ESRD headquarters in Saint Louis, MO (where it was developed).

Click here for more on Research on Buckling (more technical, but still explained without mathematical formulas).

I have been on the editorial boards of SIAM Journal on Numerical Analysis (1999-2004) and Journal of Computational and Applied Mathematics (1993-present). I have directed five doctoral dissertations. My research has been supported by the National Science Foundation and the Air Force Office of Scientific Research (AFOSR). I have been participating in the Finite Element Circus for many years. We have our own Circus Repository of Poems, poking through which may even turn up a poem penned by me.

### Research Papers

Consult my curriculum vitae.

E-mail requests for copies to me.