the Institute for Theoretical and Engineering Science
Department of Mathematics

University of Houston

Scientific Computing Seminar

Professor Roland Glowinski
Department of Mathematics
University of Houston

Numerical Investigation of a Conjecture of B.Dacorogna in Nonlinear Elasticity

Thursday, September 2
3:00 PM- 4:00 PM
Room 634 S&R1

Abstract: We investigate a numerical method for a modified conjecture of B. Dacorogna in Nonlinear Elasticity. We define the functional $J_{\gamma , f}:( W^{1,4}_0(\Omega))^2 = \mathbf{V} \rightarrow \mathbf{R}$ by

$$J_{\gamma , f}( \mathbf{v} ) = \frac {1}{4} \int_{\Omega}\vert$$$$\mbox {\boldmath$ \nabla $} \mathbf{v} \vert^4 \, dx - \frac {\g... ...2 \, dx - \int_{\Omega}\mathbf{f} \mbox {\boldmath$ \cdot $} \mathbf{v} \, dx,$$

where $\gamma$ is a positive parameter. The conjecture is that, for $\gamma _c = \frac {2} {\sqrt{3}}$, we have $\inf_{\mathbf{v} \, \epsilon \,\mathbf{V}} J_{\gamma , f}( \mathbf{v} ) = \,$ finite, if $0 \le \gamma < \gamma _c,$ and $\, = - \infty$, if $\gamma > \gamma _c$. The method includes time discretization by operator-splitting of an initial value problem associated with an Euler-Lagrange equation. At each time step, we have to solve a system of three nonlinear equations at each grid point, and a linear variational problem. The result of numerical experiments will be presented.

Future talks in Scientific Computing Seminar

$\bullet$ Sep. 23: D. Braess, the Institute of Mathematics at the Ruhr-Universitaet Bochum, Germany.

This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.