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We study the discretization of maps from a Euclidean domain into a smooth Riemannian manifold minimizing an elliptic energy. The discretization is given by a finite-dimensional approximation of the set of functions, such that the target manifold is neither embedded nor approximated. In particular, we discuss two constructions, namely geodesic and projection-based finite elements. Both have the properties needed for an error analysis comparable to standard Euclidean finite elements.
This presentation is part of Minisymposium “MS31 - Variational Approaches for Regularizing Nonlinear Geometric Data (3 parts)”
organized by: Martin Storath (Universität Heidelberg) , Martin Holler (École Polytechnique, Université Paris Saclay) , Andreas Weinmann (Hochschule Darmstadt) .