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Dissipative and Conservative Local Discontinuous Galerkin Methods for the Fornberg-Whitham Type Equations

Dissipative and Conservative Local Discontinuous Galerkin Methods for the Fornberg-Whitham Type Equations
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Year:    2021

Author:    Qian Zhang, Yan Xu, Chi-Wang Shu

Communications in Computational Physics, Vol. 30 (2021), Iss. 2 : pp. 321–356

Abstract

In this paper, we construct high order energy dissipative and conservative local discontinuous Galerkin methods for the Fornberg-Whitham type equations. We give the proofs for the dissipation and conservation for related conservative quantities. The corresponding error estimates are proved for the proposed schemes. The capability of our schemes for different types of solutions is shown via several numerical experiments. The dissipative schemes have good behavior for shock solutions, while for a long time approximation, the conservative schemes can reduce the shape error and the decay of amplitude significantly.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2020-0027

Communications in Computational Physics, Vol. 30 (2021), Iss. 2 : pp. 321–356

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    36

Keywords:    Discontinuous Galerkin method Fornberg-Whitham type equation dissipative scheme conservative scheme error estimates.

Author Details

Qian Zhang

Yan Xu

Chi-Wang Shu

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