Finite element method of BBM-Burgers equation with dissipative term based on adaptive moving mesh
type: Item
instance of: scholarly article
title: Finite element method of BBM-Burgers equation with dissipative term based on adaptive moving mesh
zbMATH Open document ID: 1402.65114
DOI: 10.1155/2017/3427376
author: Changna Lu
author: Chen Fu
author: Qian-Qian Gao
author: Hong-Wei Yang
published in: Discrete Dynamics in Nature and Society
publication date: 2018-09-27T00:00:00Z
review text: Summary: A finite element model is proposed for the Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation with a high-order dissipative term; the scheme is based on adaptive moving meshes. The model can be applied to the equations with spatial-time mixed derivatives and high-order derivative terms. In this scheme, new variables are needed to make the equation become a coupled system, and then the linear finite element method is used to discretize the spatial derivative and the fifth-order Radau IIA method is used to discretize the time derivative. The simulations of 1D and 2D BBM-Burgers equations with high-order dissipative terms are presented in numerical examples. The numerical results show that the method keeps a second-order convergence in space and provides a smaller error than that based on the fixed mesh, which demonstrates the effectiveness and feasibility of the finite element method based on the moving mesh. We also study the effect of the dissipative terms with different coefficients in the equation; by numerical simulations, we find that the dissipative term \(u_{x x}\) plays a more important role than \(u_{x x x x}\) in dissipation.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 6944815
zbMATH Keywords: finite element model
zbMATH Keywords: Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation
zbMATH Keywords: fifth-order Radau IIA method
zbMATH Keywords: moving mesh
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/3427376
OpenAlex ID: W2772452635
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description: scientific article; zbMATH DE number 6944815