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Numerics for surfaces and interfaces May 03, 2011 (10:00 AM PDT - 12:00 PM PDT)
Parent Program: --
Location: MSRI: Simons Auditorium
Speaker(s) Charles Elliott (University of Warwick)
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Our goal is to formulate a methodology for solving PDEs for and on evolving surfaces. In the first part I will discuss the problem of minimizing a Helfrich (Willmore) type energy coupled to a surface Cahn Hilliard energy. This is a model for two phase biomembranes which form the boundary of a vesicle.The surface PDEs characterising a minimizer will be derived. Using gradient flow I will show how one may seek minimizers by looking for stationary solutions of a geometric fourth order evolution PDE for an evolving surface whose motion is coupled to an equation of Allen-Cahn type on that surface. One may view this as an example of a free boundary on a free boundary.

In the second part I will discuss numerical methods based on phase field models and surface finite elements. In particular I will describe double obstacle phase field models and the evolving surface finite element method.

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