### Thursday, July 16

## MS50

Least-Squares Finite, Element Methods: Theory and Applications (Part I of II)

10:30 AM-12:30 PM

*Room: Sidney Smith 2118*

As a rule, variational formulations of systems of partial differential equations (for example, the Stokes problem) lead 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 of least-squares type. Such methods involve minimization of problem-dependent least-squares functionals and offer many attractive theoretical and computational advantages that are not present in other discretization schemes, e.g., mixed Galerkin methods. Most notably, least-squares methods circumvent stability conditions such as the inf-sup condition, lead to symmetric and positive definite algebraic systems, and allow one to enforce essential boundary conditions in a weak, variational sense.

The speakers in this minisymposium will present new results in mathematical approaches, numerical algorithms and applications of least squares methods. This minisymposium will bring together experts in the field with extensive applied and industrial background and will provide the audience with a broad perspective of the current state of the theory and applications of least squares.

See Part II, MS56.

**Organizer: Pavel B. Bochev**

*University of Texas, Arlington*
**10:30 A Negative Norm Least Squares Approach to Div-Curl Systems in Two and Three Dimensions**
*James Bramble* and Xuejun Zhang, Texas A&M University, College Station
**11:00 Analysis and Numerical Experiments in 2 and 3-D by Piecewise Linear Element to Stokes with Velocity Boundary Condition**
- Ching L. Chang, Cleveland State University
**11:30 Adaptive Refinement and Singular Functions with First-Order Systems Least Squares Functionals**
*Thomas A. Manteuffel*, Markus Berndt, Steve McCormick, and Gerhard Starke, University of Colorado, Boulder
**12:00 Least-Squares Solution of Boundary Value Problems**
*George Pinder*, J. P. Laible and D. G. Zeitoun, University of Vermont

LMH Created: 3/18/98; MMD Updated: 6/22/98