| Issue |
ESAIM: M2AN
Volume 59, Number 5, September-October 2025
|
|
|---|---|---|
| Page(s) | 2447 - 2490 | |
| DOI | https://doi.org/10.1051/m2an/2025056 | |
| Published online | 17 September 2025 | |
Unconditionally stable space–time isogeometric discretization for the wave equation in Hamiltonian formulation
1
Fakult¨at für Mathematik, Universit¨at Wien, 1090 Vienna, Austria
2
Dipartimento di Matematica “Felice Casorati”, Università di Pavia, 27100 Pavia, Italy
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
1
November
2024
Accepted:
23
June
2025
We consider a family of conforming space–time discretizations for the wave equation based on a first-order-in-time formulation employing maximal regularity splines. In contrast with second-order-in-time formulations, which require a CFL condition to guarantee stability, the methods we consider here are unconditionally stable without the need for stabilization terms. Along the lines of the work by Ferrari and Fraschini [Math. Comput. (2025)], we address the stability analysis by studying the properties of the condition number of a family of matrices associated with the time discretization. Numerical tests validate the performance of the method.
Mathematics Subject Classification: 65M60 / 15A12 / 65L60 / 15B05
Key words: Wave equation / space–time method / splines / Toeplitz matrices
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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