A parameter-free adaptivity indicator for a p-adaptive discontinuous Galerkin discretization of the shallow water equations

Title data

Faghih-Naini, Sara ; Aizinger, Vadym ; Kuckuk, Sebastian ; Angersbach, Richard:
A parameter-free adaptivity indicator for a p-adaptive discontinuous Galerkin discretization of the shallow water equations.
2023
Event: SIAM Conference on Mathematical & Computational Issues in the Geosciences (GS23) , 19.-22. June 2023 , Bergen, Norway.
(Conference item: Conference , Speech )

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Abstract in another language

We propose a parameter-free adaptivity indicator for a p-adaptive quadrature-free discontinuous Galerkin discretization of the shallow water equations.
It aims to identify resolved and under-resolved solution parts while distinguishing between smooth and non-smooth regions without utilizing any problem-dependent parameters. The information collected for slope limiting is used to detect the error and smoothness of the solution. For piecewise constant discretizations, the indicator first performs a reconstruction procedure.
The accuracy and robustness of the new scheme are evaluated using several benchmarks from the literature and compared to other adaptivity indicators. Our results indicate that the proposed indicator finds a good balance between solution quality and computational overhead.