Speaker: Max Gunzburger
Title: Least-squares finite element methods with applications.
Affiliation: Iowa State University.
Date: Friday, October 5, 2001.
Place and Time: Room 101 - Love Building, 3:30 pm.
Refreshments: Room 104 - Love Building, 3:00 pm.

Abstract. Least-squares finite element methods offer the promise of providing a Rayleigh-Ritz type setting for any partial differential equation problem. However, to realize that promise, one must make a number of choices and balance the desire for practicality with that for mathematical well-posedeness. We begin by briefly going through a taxonomy of finite element methods, ranging from the those based on convex optimization principles, through mixed and Galerkin methods, and ending with modifications proposed for the latter which aim to improve stability and efficiency. This discussion motivates the need for least-squares finite element methods. We then discuss a unified theoretical framework for least-squares finite element methods, show how choices are made within the framework, and show how the framework applies to specific problems, most notably the Stokes equations.