| Issue |
ESAIM: M2AN
Volume 60, Number 2, March-April 2026
|
|
|---|---|---|
| Page(s) | 495 - 515 | |
| DOI | https://doi.org/10.1051/m2an/2026009 | |
| Published online | 24 March 2026 | |
Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators
1
School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, P.R. China
2
Department of Mathematics, University of Innsbruck, 6020 Innsbruck, Austria
3
Digital Science Center, University of Innsbruck, 6020 Innsbruck, Austria
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
7
July
2025
Accepted:
21
January
2026
Abstract
We derive rigorous error bounds for exponential Runge-Kutta discretizations of parabolic equations with nonsmooth initial data. Our analysis is carried out in the framework of abstract semi-linear evolution equations, allowing for operators with non-dense domains. The results provide a foundation for establishing error estimates for nonsmooth data in prototypical problems such as the Allen-Cahn and Burgers equations. Furthermore, we apply these estimates to the analysis of split exponential integrators, yielding convergence results expressed explicitly in terms of the prescribed data.
Mathematics Subject Classification: 65M12 / 65L06
Key words: Exponential Runge-Kutta methods / semilinear parabolic problems / nonsmooth initial data / split exponential integrators
© The authors. Published by EDP Sciences, SMAI 2026
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