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

Title data

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. Vol. 13 (2022) Issue 1 . - No. 18.
ISSN 1869-2672
DOI: https://doi.org/10.1007/s13137-022-00208-3

Official URL: Volltext

Project information

Project title:
Project's official titleProject's id
Performance optimized software strategies for unstructured-mesh applications in ocean modelingAI 117/6-1

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: s p-adaptivity; Error and smoothness indicator; Discontinuous Galerkin method; Quadrature-free; Shallow water equations; Ocean modeling
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Scientific Computing
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Scientific Computing > Chair Scientific Computing - Univ.-Prof. Dr. Mario Bebendorf
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professor Numerics of Partial Differential Equations
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professor Numerics of Partial Differential Equations > Professor Numerics of Partial Differential Equations - Univ.-Prof. Dr. Vadym Aizinger
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Research Institutions > Research Centres > Forschungszentrum für Wissenschaftliches Rechnen an der Universität Bayreuth - HPC-Forschungszentrum
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Profile Fields
Profile Fields > Advanced Fields
Research Institutions
Research Institutions > Research Centres
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
000 Computer Science, information, general works > 010 Bibliography
500 Science > 510 Mathematics
500 Science > 550 Earth sciences, geology
600 Technology, medicine, applied sciences
600 Technology, medicine, applied sciences > 600 Technology
Date Deposited: 14 Oct 2022 07:02
Last Modified: 14 Oct 2022 07:57
URI: https://eref.uni-bayreuth.de/id/eprint/72428