For more information about this meeting, contact Xiantao Li, Yuxi Zheng, Kris Jenssen, Jinchao Xu, Hope Shaffer.
| Title: | Geometric variational crimes: Hilbert complexes, finite element exterior calculus, and problems on hypersurfaces |
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| Seminar: | Computational and Applied Mathematics Colloquium |
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| Speaker: | Ari Stern, UC San Diego |
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| Abstract: |
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| In recent years, the success of "mixed" finite element methods has
been shown to have surprising connections with differential geometry
and algebraic topology---particularly with the calculus of exterior
differential forms, de Rham cohomology, and Hodge theory. In this
talk, I will discuss how the notion of "Hilbert complex," rather than
"Hilbert space," provides the appropriate functional-analytic setting
for the numerical analysis of these methods. Furthermore, I will
present some recent results that analyze "variational crimes" (a la
Strang) on Hilbert complexes, allowing the numerical analysis to be
extended from polyhedral regions in Euclidean space to problems on
arbitrary Riemannian manifolds. As a direct consequence, this
analysis also generalizes several key results on "surface finite
element methods" for the approximation of elliptic PDEs on
hypersurfaces (e.g., membranes or level sets undergoing geometric
evolution). |
Room Reservation Information
| Room Number: | MB106 |
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| Date: | 05 / 06 / 2011 |
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| Time: | 03:35pm - 04:25pm |
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