Repository: Freie Universität Berlin, Math Department

Geodesic finite elements in spaces of zero curvature

Sander, O. (2013) Geodesic finite elements in spaces of zero curvature. In: Numerical Mathematics and Advanced Applications 2011. Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011 . Springer Berlin Heidelberg, pp. 449-457. ISBN 978-3-642-33133-6


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We investigate geodesic finite elements for functions with values in a space of zero curvature, like a torus or the Möbius strip. Unlike in the general case, a closed-form expression for geodesic finite element functions is then available. This simplifies computations, and allows us to prove optimal estimates for the interpolation error in 1d and 2d. We also show the somewhat surprising result that the discretization by Kirchhoff transformation of the Richards equation proposed in Berninger et al. (SIAM J Numer Anal 49(6):2576–2597, 2011) is a discretization by geodesic finite elements in the manifold R with a special metric.

Item Type:Book Section
Subjects:Mathematical and Computer Sciences > Mathematics > Numerical Analysis
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:1818
Deposited By: Ekaterina Engel
Deposited On:23 Feb 2016 10:05
Last Modified:03 Mar 2017 14:42

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