Geodesic Finite Elements in Spaces of Zero Curvature
Please always quote using this URN:urn:nbn:de:0296-matheon-9005
- We investigate geodesic finite elements for functions with values in a space of zero curvature, like a torus or the M\"obius 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 by Berninger et al. is a discretization by geodesic finite elements in the manifold $\mathbb{R}$ with a special metric.
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| Author: | Oliver Sander |
|---|---|
| URN: | urn:nbn:de:0296-matheon-9005 |
| Referee: | Peter Deuflhard |
| Document Type: | Preprint, Research Center Matheon |
| Language: | English |
| Date of first Publication: | 2011/09/23 |
| Release Date: | 2011/09/23 |
| Tag: | Richards equation; explicit formula; geodesic finite elements; interpolation error; zero curvature |
| Institute: | Freie Universität Berlin |
| Project: | A Life sciences |
| MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods |
| 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems | |
| Preprint Number: | 818 |
