p-adaptive discontinuous Galerkin method for the shallow water equations with a parameter-free error indicator

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Faghih-Naini, Sara ; Aizinger, Vadym:
p-adaptive discontinuous Galerkin method for the shallow water equations with a parameter-free error indicator.
In: GEM : International Journal on Geomathematics. Bd. 13 (2022) Heft 1 . - 18.
ISSN 1869-2672
DOI: https://doi.org/10.1007/s13137-022-00208-3

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Abstract

We propose a p-adaptive quadrature-free discontinuous Galerkin method for the shallow water equations based on a computationally efficient adaptivity indicator which works without any problem-dependent parameters. The error and smoothness of the solution are detected using the information collected for slope limiting and, for piecewise constant discretizations, by carrying out a reconstruction procedure. The accuracy and robustness of the new scheme are evaluated using several benchmarks and compared to other adaptivity indicators. Our results indicate that the proposed indicator finds a good balance between solution quality and computational overhead.