Quasi-optimal error estimates for the approximation of stable harmonic maps
Numerical Analysis
2022-09-27 v1 Numerical Analysis
Abstract
Based on a quantitative version of the inverse function theorem and an appropriate saddle-point formulation we derive a quasi-optimal error estimate for the finite element approximation of harmonic maps into spheres with a nodal discretization of the unit-length constraint. The estimate holds under natural regularity requirements and appropriate geometric stability conditions on solutions. Extensions to other target manifolds including boundaries of ellipsoids are discussed.
Cite
@article{arxiv.2209.11985,
title = {Quasi-optimal error estimates for the approximation of stable harmonic maps},
author = {Sören Bartels and Christian Palus and Zhangxian Wang},
journal= {arXiv preprint arXiv:2209.11985},
year = {2022}
}
Comments
18 pages