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Journal of Scientific Computing

Erschienen in:

20.03.2019

Analysis and Entropy Stability of the Line-Based Discontinuous Galerkin Method

verfasst von: Will Pazner, Per-Olof Persson

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2019

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Abstract

We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions, this method guarantees that the discrete integral of the entropy is non-increasing. This nonlinear entropy stability property is important for the robustness of the method, in particular when applied to problems with discontinuous solutions or when the mesh is under-resolved. This line-based method is significantly less computationally expensive than a standard DG method. Numerical results are shown demonstrating the effectiveness of the method on a variety of test cases, including Burgers’ equation and the Euler equations, in one, two, and three spatial dimensions.

Vorheriger Artikel Dynamic Programming for Finite Ensembles of Nanomagnetic Particles

Nächster Artikel Linearized Galerkin FEMs for Nonlinear Time Fractional Parabolic Problems with Non-smooth Solutions in Time Direction

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Titel: Analysis and Entropy Stability of the Line-Based Discontinuous Galerkin Method
verfasst von: Will Pazner
Per-Olof Persson
Publikationsdatum: 20.03.2019
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2019
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-019-00942-1

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