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Invitation to the Mathematical Colloquium
Monday, December 11, 2023, conference room (R107), 5 p.m. c. t.
Prof. Dr. Jan Giesselmann , AG Numerik und Wissenschaftliches Rechnen der TU Darmstadt talks about the topic: " On the connection between well-posedness theory and a posteriori error estimates for numerical methods on the example of hyperbolic systems"
Abstract: In this talk we will review some results on rigorous a posteriori error estimates for numerical approximations of systems of hyperbolic conservation laws, i.e. bounds for discretization errors that can be computed from numerical solutions without making assumption of the properties of the exact solution. We will explain the fundamental link between a posteriori error estimates and stability properties of the PDE that is to be approximated.
We will describe a posteriori error estimates that have been derived a few years ago based on relative entropy stability estimates. In addition, we will outline recent progress in a posteriori error estimates for one-dimensional hyperbolic conservation laws based on two approaches: Firstly, results using Bressan's stability theory and, secondly, results using a-contraction estimates.
Starting at 16:45, there will be an opportunity for all interested parties to talk over coffee and tea in the meeting room (R206).
Olaf Ippisch
Organizer: Institute of Mathematics, Erzstraße 1, 38678 Clausthal-Zellerfeld