NAMColloquium On the design and analysis of property-preserving finite element schemes for hyperbolic conservation laws |  |
Speaker:Prof. Dr. Dmitri Kuzmin, Technische Universität Dortmund
Organizer:Institut für Numerische und Angewandte Mathematik
Details:
This talk presents a family of algebraically constrained finite element schemes for nonlinear hyperbolic problems. The validity of (generalized) discrete maximum principles is enforced using monolithic convex limiting, a new flux correction procedure based on representation of spatial semi-discretizations in terms of admissible intermediate states. Limiter-based entropy fixes are performed to ensure entropy stability. After explaining the design philosophy behind our flux-corrected finite element approximations and showing some numerical examples, we turn to the analysis of consistency and convergence. In particular, we prove a Lax-Wendroff-type theorem for the inequality-constrained semi-discrete problem. A key component of our analysis is the use of a weak estimate on bounded variation, which follows from the semi-discrete entropy stability property of the method under investigation. For the Euler equations of gas dynamics, we prove weak convergence to a dissipative weak solution.
The convergence analysis to be presented in this talk is joint work with Maria Lukáčová-Medvid’ová and Philipp Öffner.
The convergence analysis to be presented in this talk is joint work with Maria Lukáčová-Medvid’ová and Philipp Öffner.
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Type:Colloquium
Language:English
Category:Research
Host:Prof. Dr. Gert Lube
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Direct link to event:https://events.goettingen-campus.de/event?eventId=10216901
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