| Speaker: | Ricardo Nochetto, University of Maryland |
| Title: | Adaptive FEM for the Laplace-Beltrami Operator and Applications to Geometric Flows |
| Time: | 3:00-4:00 pm |
| Place: | Blocker 628 |
The Laplace-Beltrami operator, or surface Laplacian, is ubiquitous in geometric problems and has a natural variational structure. This allows for finite element discretizations of surface and PDE of arbitrary polynomial degree, and the use of refinement/coarsening techniques that lead to adaptivity. We first discuss key properties and present applications such as surface diffusion, optimal shape control and image segmentation, along with several simulations exhibiting large deformations as well as pinching and topological changes in finite time. This part is joint with G. Dogan, P. Morin and M. Verani. We next discuss a posteriori error analysis for the Laplace-Beltrami operator and prove a conditional contraction property of the ensuing AFEM; this is joint with K. Mekchay and P. Morin. We finally discuss the geometrically consistent refinement of polyhedral surfaces, which is critical for large domain deformations and new paradigm in adaptivity. This is joint with A. Bonito and M.S. Pauletti.
Last revised: 03/31/08 By: abnersg@math