Wednesday 10 September 2025, at 3:30 pm in Room 3014 (3rd Floor - U5 Building), Prof. Aleksey Sikstel (University of Cologne) will hold the following talk
Title: A posteriori error estimates for high order approximations of hyperbolic conservation laws
Abstract: We prove rigorous a posteriori error estimates for high order Runge-Kutta discontinuous Galerkin (RKDG) schemes for nonlinear systems of hyperbolic conservation laws in one spatial dimension. The estimates are based on recent results for first-order finite volume schemes [1]. Our estimators rely on recent stability results by Bressan, Chiri and Shen [2], a new way to localize residuals and a novel method to compute dual norms of these local residuals. Computing dual norms becomes possible by a reconstruction of the RKDG solution continuously within space-time cells and a direct approximation of the localized residual.
References
[1] J. Giesselmann and A. Sikstel. A-posteriori error estimates for systems of hyperbolic conservation laws via computing negative norms of local residuals. IMA Journal of Numerical Analysis, page drae111, 03 2025.
[2] A. Bressan, M. T. Chiri, and W. Shen. A posteriori error estimates for numerical solutions to hyperbolic conservation laws. Archive for Rational Mechanics and Analysis, 241(1):357–402, July 2021.
*in collaboration with Jan Giesselmann.
All interested are invited to participate