Author:
Giesselmann Jan,Mäder-Baumdicker Elena,Stonner David Jakob
Abstract
AbstractWe provide a posteriori error estimates in the energy norm for temporal semi-discretisations of wave maps into spheres that are based on the angular momentum formulation. Our analysis is based on novel weak–strong stability estimates which we combine with suitable reconstructions of the numerical solution. We present time-adaptive numerical simulations based on the a posteriori error estimators for solutions involving blow-up.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics
Reference38 articles.
1. Aitchison, I.J.R., Hey, A.J.G.: Gauge theories in particle physics: Volume I: From Relativistic Quantum Mechanics to QED, 3rd edn. Graduate Student Series in Physics
2. Carroll, S.M.: Spacetime and geometry: an introduction to general relativity. Cambridge University Press, Cambridge (2019) https://doi.org/10.1017/9781108770385
3. Shatah, J., Struwe, M.: Geometric wave equations, vol. 2, p. 153. New York University, Courant Institute of Mathematical Sciences, New York, NY (1998)
4. Tataru, D.: The wave maps equation. Bull. Amer. Math. Soc. (N.S.) 41(2), 185–204 (2004)
5. Krieger, J.: Global regularity and singularity development for wave maps. In: Surveys in differential geometry. Vol. XII. Geometric flows. Survey Differential Geometry, vol. 12, pp. 167–201. International Press