TY - GEN A1 - Sander, Oliver T1 - Geodesic Finite Elements in Spaces of Zero Curvature N2 - 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. KW - geodesic finite elements KW - zero curvature KW - explicit formula KW - interpolation error KW - Richards equation Y1 - 2011 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/900 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-9005 ER -