Fully Discrete High-Order DG Scheme for Waves: Dispersion and Observability
Li Y, Wang X, Zuazua E (2026)
Publication Language: English
Publication Status: Submitted
Publication Type: Unpublished / Preprint
Future Publication Type: Journal article
Publication year: 2026
DOI: 10.48550/arXiv.2605.17464
Open Access Link: https://doi.org/10.48550/arXiv.2605.17464
Abstract
This paper investigates the spectral structure, numerical dispersion, and observability of fully discrete approximations of the one-dimensional wave equation by Pk (local) discontinuous Galerkin methods. Characterizing the coupled space-time numerical dispersion reveals a trapping mechanism that forces the group velocities of both physical and spurious modes to vanish at selected frequencies. We then establish an exponential blow-up of order exp(h−(1−ε)) for the observability constant under this trapping mechanism. To overcome this divergence for arbitrary k, we propose a spectral filtering strategy to restore uniform observability. Theoretical analysis and numerical experiments indicate that higher-order methods may facilitate this recovery by preserving a larger genuine physical frequency band, thereby reducing filtering cost and observation time.
Authors with CRIS profile
Enrique Zuazua Iriondo
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
China (CN)How to cite
APA:
Li, Y., Wang, X., & Zuazua, E. (2026). Fully Discrete High-Order DG Scheme for Waves: Dispersion and Observability. (Unpublished, Submitted).
MLA:
Li, Yunzhang, Xiaoyang Wang, and Enrique Zuazua. Fully Discrete High-Order DG Scheme for Waves: Dispersion and Observability. Unpublished, Submitted. 2026.
BibTeX: Download