The geometry of convergence in numerical analysis
arXiv:1909.11183
Abstract
The domains of mesh functions are strict subsets of the underlying space of continuous independent variables. Spaces of partial maps between topological spaces admit topologies which do not depend on any metric. Such topologies geometrically generalize the usual numerical analysis definitions of convergence.
13 pages, 2 figures. This version is a metadata update only. A revision has been accepted in the Journal of Computational Dynamics