Nonlinear PDE Days           Karlsruhe               January  20 – 21,  2011





Gerd Dziuk

University of Freiburg, Germany



Discretization of the anisotropic Willmore functional


The discretization of geometric functionals is needed for simulations in mathematics and applied sciences. 
The Willmore functional is an important "higher order" functional. In this lecture we discuss the classical Willmore 
functional and its anisotropic generalization. The discretization with Finite Elements is derived with the help of 
adequate discrete transport formulae. They allow the calculation of first and second variation of discretized functionals 
in a form which is very useful for numerical computations and which directly give stability for the spatially discretized 
related geometric flows. We discuss anisotropic geometric functionals in some detail and show how they can be 
discretized by finite elements. 
This is joint work with P. Pozzi (Freiburg).




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