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On nonlinear artificial viscosity, discrete maximum principle and hyperbolic conservation laws
journal contribution
posted on 2023-06-08, 08:16 authored by Erik BurmanA finite element method for Burgers equation is studied. The method is analyzed using techniques from stabilized finite element methods and convergence to entropy solutions is proven under certain hypotheses on the artificial viscosity. In particular we assume that a discrete maximum principle holds. We then construct a nonlinear artificial viscosity that satisfies the assumptions required for convergence and that can be tuned to minimize artificial viscosity away from local extrema. The theoretical results are exemplified on a numerical example.
History
Publication status
- Published
Journal
BIT Numerical MathematicsISSN
0006-3835Publisher
Springer VerlagExternal DOI
Issue
4Volume
47Page range
715-733Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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