Thursday, July 17

3:15 PM-5:15 PM
Building 300, Room 300

MS69
Applications of the Least Squares Finite Element Methods

Recently, there has been substantial interest in the use of least-squares principles for the approximate solution of incompressible flow problems. These works introduce extra equations in the velocity-vorticity-pressure equations such that the resulting first order systems are elliptic.They have been proven very effective for the incompressible flow problems. However, following the framework introduced by Fix, Gunzburger and Nicolaides, the least-squares scheme was modified to resolve difficulties in solving convection dominated, large deformation and free boundary problems. Recent results will be presented in the minisymposium to illustrate the robustness and effectiveness of the least-squares schemes.

Fix, Lee and Chen have been working in the applications of the least-squares schemes for decades. This minisymposium will provide an opportunity for them to discuss further directions of joint research in these areas. In addition, it will illustrate the great potential of the least-squares methods to different fields of engineering, in particular, fluid and solid mechanics.

Organizer: Tsu-Fen Chen
National Chung Cheng University, Taiwan

3:15 Least Squares Finite Element Methods for Free Boundary Problems

George J. Fix, University of Texas, Arlington

3:45 Multilevel Solutions and Optimal Adaptive Grids for Convection-Diffusion Problems

Tsu-Fen Chen, Organizer; and Chen-Yao G. Lai, National Chung Cheng University, Taiwan

4:15 A Direct Finite Element Approach to Inelastic Large Deformation Problems

Y.-K. Lee, TRW Vehicle Safety Systems Inc., Washington, MI

4:45 Simulation of Immiscible Displacement Using Least Squares Finite Element Methods

Tsu-Fen Chen, Organizer

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