Wednesday, July 16

10:30 AM-12:30 PM
Building 320, Room 105

Recent Development and Applications of Least-Squares Finite Element Methods

Least-squares finite element methods are versatile and stable, they can be used to solve a variety of problems associated with elasticity, fluid flow, and wave propagation without any ad-hoc treatment. However, before they can be applied routinely to real world problems, issues pertaining to accuracy, implementation and performance must be addressed. These will be the focus of the proposed minisymposium. The speakers will provide a complete picture of the potential and capabilities offered by least-squares finite element methods. Most exiting finite element methods generate a system of linear algebraic equations that is non-symmetric and indefinite. These characteristics call for direct solution methods which are computationally expensive and cannot be easily applied to large scale three-dimensional problems. Least-squares finite element methods do not suffer from this drawback, the resulting system of equations is symmetric, positive definite, and facilitates the application of fast multigrid methods. We expect to establish a collaborative effort between academe and industry to develop an accurate and efficient finite element method for large-scale simulations.

Organizers: Daniel C. Chan, Boeing North American, Rocketdyne Division; and Zhiqiang Cai, Purdue University, West Lafayette

10:30 Least-Squares Finite Element Methods: Analysis and Implementation
Max D. Gunzburger, Iowa State University
11:00 Recent Development in First-Order Systems Least-Squares Formulation
Tom Manteuffel, University of Colorado, Boulder
11:30 Title to be determined
James H. Bramble, Texas A&M University, College Station
12:00 A Least-Squares Spectral Element Method for Incompressible Navier-Stokes Equations
Daniel C. Chan, Organizer

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TMP, 4/4/97 tjf, 5/28/97