Oberseminar Numerische Mathematik / Scientific Computing
Hans Fritz
Universität Freiburg
Isoparametric finite element approximation of Ricci curvature
Abstract:
The surface finite element approach have been used to approximate curvatures on hypersurfaces and to discretize geometrical PDE’s. In my talk I will present a definition of discrete Ricci curvature on triangulated hypersurfaces based on a weak formulation. In the two and three dimensional case it is possible to prove that the convergence in the L2-norm is linear for a quadratic approximation of the hypersurface with isoparametric finite elements. By using a smoothing scheme in the case of a linear approximation of the hypersurface we still get a convergence of order 2/3 in the L2-norm and of order 1/3 in the W1;2-norm.
| Datum: | 14.02.11 | Zeit: | 17:00 Uhr | Ort: | FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin. | Raum: | 031 im Erdgeschoss |