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- W2152394501 abstract "SUMMARY We introduce geodesic finite elements as a conforming way to discretize partial differential equations for functions v : Ω → M , where Ω is an open subset of and M is a Riemannian manifold. These geodesic finite elements naturally generalize standard first‐order finite elements for Euclidean spaces. They also generalize the geodesic finite elements proposed for d = 1 in a previous publication of 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 trust‐region 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 to S 2 . Copyright © 2012 John Wiley & Sons, Ltd." @default.
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- W2152394501 date "2012-06-22" @default.
- W2152394501 modified "2023-10-10" @default.
- W2152394501 title "Geodesic finite elements on simplicial grids" @default.
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- W2152394501 doi "https://doi.org/10.1002/nme.4366" @default.
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