**Tuesday Afternoon, October 24**
## MS19

Least Squares Finite Element Methods

Frequently, variational formulation of systems of partial differential
equations (for example, Stokes problem) leads to saddle-point optimization
problems. Although approximation of such problems is now well understood,
their numerical solution may still be difficult and computationally demanding.
This minisymposium will focus on important new developments in finite element
methods that use least squares variational principles. Such methods possess
valuable theoretical and computational properties: they avoid saddle-point,
circumvent the inf-sup condition and lead to symmetric, positive definite
algebraic systems. The speakers in this minisymposium will present new results
in mathematical approaches, numerical algorithms and applications of least
squares methods, paying special attention to implementation issues and numerical
algorithms. The speakers will also report on recent experiences with industrial
applications of least squares methods involving fluid flow and transport
problems, linear elasticity and semi-conductor design.
Organizer: Pavel B. Bochev

University of Texas, Arlington

**12:30 Analysis of Weighted Least Squares Methods**
*Max D. Gunzburger*, Virginia Polytechnic Institute and State University; and Pavel Bochev, Organizer

**1:00 A Least Squares Finite Element Method for Fluid Dynamics and Transport Processes**
- Tate T.H. Tsang, University of Kentucky

**1:30 A Least Squares Method for the Stokes Equations Which Does Not Require Additional Variables**
- James H. Bramble, Texas A&M University, College Station; and
* Joseph Pasciak*, Brookhaven National Laboratory

**2:00 First-Order Systems Least Squares: A Methodology for Solving Systems of PDEs **
- Thomas A. Manteuffel, University of Colorado, Boulder

**2:30 Least Squares Finite Element Methods for Free Boundary Problems Arising in Semiconductor Design**
- George J. Fix, University of Texas, Arlington

7/26/95