A posteriori error estimates for wave maps into spheres
Jan Giesselmann, Elena M\"ader-Baumdicker, David Jakob Stonner
TL;DR
This paper develops a posteriori error estimates for wave maps into spheres using the angular momentum formulation, enabling adaptive time-stepping in simulations, including those with blow-up phenomena.
Contribution
It introduces novel weak-strong stability estimates and combines them with solution reconstructions for improved error estimation in wave map simulations.
Findings
Effective a posteriori error estimators for wave maps
Successful adaptive simulations capturing blow-up behavior
Enhanced stability analysis for numerical methods
Abstract
We 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSeismic Imaging and Inversion Techniques · Meteorological Phenomena and Simulations · Advanced Numerical Methods in Computational Mathematics