Tuesday Afternoon, October 24

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

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