New Conservative Finite Volume Element Schemes for the Modified Regularized Long Wave Equation

New Conservative Finite Volume Element Schemes for the Modified Regularized Long Wave Equation

Year:    2017

Author:    Jinliang Yan, Ming-Chih Lai, Zhilin Li, Zhiyue Zhang

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 2 : pp. 250–271

Abstract

In this paper, we propose a new energy-preserving scheme and a new momentum-preserving scheme for the modified regularized long wave equation. The proposed schemes are designed by using the discrete variational derivative method and the finite volume element method. For comparison, we also propose a finite volume element scheme. The conservation properties of the proposed schemes are analyzed and we find that the energy-preserving scheme can precisely conserve the discrete total mass and total energy, the momentum-preserving scheme can precisely conserve the discrete total mass and total momentum, while the finite volume element scheme merely conserve the discrete total mass. We also analyze their linear stability property using the Von Neumann theory and find that the proposed schemes are unconditionally linear stable. Finally, we present some numerical examples to illustrate the effectiveness of the proposed schemes.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2014.m888

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 2 : pp. 250–271

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Energy momentum mass finite volume element method MRLW equation.

Author Details

Jinliang Yan

Ming-Chih Lai

Zhilin Li

Zhiyue Zhang

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