Sander, O. (2012) Geodesic finite elements on simplicial grids. International Journal for Numerical Methods in Engeneering, 92 (12). pp. 9991025. ISSN Online: 10970207

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Official URL: https://dx.doi.org/10.1002/nme.4366
Abstract
We introduce geodesic finite elements as a conforming way to discretize partial differential equations for functions $v : \Omega \to M$, where $\Omega$ is an open subset of $\R^d$ and $M$ is a Riemannian manifold. These geodesic finite elements naturally generalize standard firstorder finite elements for Euclidean spaces. They also generalize the geodesic finite elements proposed for $d=1$ by the author. Our formulation is equivariant under isometries of $M$, and hence preserves objectivity of continuous problem formulations. We concentrate on partial differential equations that can be formulated as minimization problems. Discretization leads to algebraic minimization problems on product manifolds $M^n$. These can be solved efficiently using a Riemannian trustregion method. We propose a monotone multigrid method to solve the constrained inner problems with linear multigrid speed. As an example we numerically compute harmonic maps from a domain in $\R^3$ to $S^2$.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Numerical Analysis 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  1868 
Deposited By:  Ekaterina Engel 
Deposited On:  30 Mar 2016 17:49 
Last Modified:  03 Mar 2017 14:42 
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