Graduate Seminar "Aktuelle Themen der Numerik"

 

Thursday, Jan 23, 2014, 02:00 pm

Approximation of Gradient Flows on Riemannian manifolds using Geodesic Finite Elements

Hanne Hardering (FU Berlin)

Abstract:
Geodesic Finite Elements (GFEs) have been introduced recently to approximate solutions of energy minimization problems of functions which take their values on a Riemannian manifold without making use of an embedding into Euclidean space.
In joint work with O. Sander and P. Grohs a first discretization error analysis for $H ^1$-elliptic energies has been developed showing that under certain conditions GFEs have the same approximation quality as Finite Elements in Euclidean space. In this talk we will discuss the generalization of the horizontal line method in order to approximate $L ^2$-gradient flows of the aforementioned elliptic energies using GFEs as space discretization scheme. This allows for example the intrinsic discretization of the harmonic map heat flow, in particular under conditions similar to settings where unique solvability of the analytic problem can be established.

Time: 02:00 pm

Location: Room 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen