Thursday, July 16

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

Program Program Overview Program-at-a-Glance Program Updates Speaker Index Registration Hotel Transportation

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