# Discrete Topology-Revealing Vector Fields on Simplicial Surfaces with Boundary

@inproceedings{Poelke2017DiscreteTV, title={Discrete Topology-Revealing Vector Fields on Simplicial Surfaces with Boundary}, author={Konstantin Poelke and Konrad Polthier}, year={2017} }

We present a discrete Hodge-Morrey-Friedrichs decomposition for piecewise constant vector fields on simplicial surfaces with boundary which is structurally consistent with the smooth theory. In particular, it preserves a deep linkage between metric properties of the spaces of harmonic Dirichlet and Neumann fields and the topology of the underlying geometry, which reveals itself as a discrete de Rham theorem and a certain angle between Dirichlet and Neumann fields. We illustrate and discuss this…

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