Volume 10, Issue 1
Streamline Diffusion Virtual Element Method for Convection-Dominated Diffusion Problems

East Asian J. Appl. Math., 10 (2020), pp. 158-180.

Published online: 2020-01

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• Abstract

A novel streamline diffusion form of virtual element method for convectiondominated diffusion problems is studied. The main feature of the method is that the test function in the stabilised term has the adjoint operator-like form (−∇·($K$(x)∇$v$)b(x)·∇$v$). Unlike the standard VEM, the stabilisation scheme can effificiently avoid nonphysical oscillations. The well-posedness of the problem is also proven and error estimates are provided. Numerical examples show the stability of the method for very large Péclet numbers and its applicability to boundary layer problem.

• Keywords

Convection dominated diffusion problem, streamline diffusion virtual element method, stabilisation, optimal convergence, boundary layer problem.

65N12, 76R99

lyx29cherish@163.com (Yuxia Li)

xiecong121@163.com (Cong Xie)

fxlmath@xju.edu.cn (Xinlong Feng)

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@Article{EAJAM-10-158, author = {Li , Yuxia and Xie , Cong and Feng , Xinlong }, title = {Streamline Diffusion Virtual Element Method for Convection-Dominated Diffusion Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {1}, pages = {158--180}, abstract = {

A novel streamline diffusion form of virtual element method for convectiondominated diffusion problems is studied. The main feature of the method is that the test function in the stabilised term has the adjoint operator-like form (−∇·($K$(x)∇$v$)b(x)·∇$v$). Unlike the standard VEM, the stabilisation scheme can effificiently avoid nonphysical oscillations. The well-posedness of the problem is also proven and error estimates are provided. Numerical examples show the stability of the method for very large Péclet numbers and its applicability to boundary layer problem.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.231118.240619}, url = {http://global-sci.org/intro/article_detail/eajam/13608.html} }
TY - JOUR T1 - Streamline Diffusion Virtual Element Method for Convection-Dominated Diffusion Problems AU - Li , Yuxia AU - Xie , Cong AU - Feng , Xinlong JO - East Asian Journal on Applied Mathematics VL - 1 SP - 158 EP - 180 PY - 2020 DA - 2020/01 SN - 10 DO - http://dor.org/10.4208/eajam.231118.240619 UR - https://global-sci.org/intro/article_detail/eajam/13608.html KW - Convection dominated diffusion problem, streamline diffusion virtual element method, stabilisation, optimal convergence, boundary layer problem. AB -

A novel streamline diffusion form of virtual element method for convectiondominated diffusion problems is studied. The main feature of the method is that the test function in the stabilised term has the adjoint operator-like form (−∇·($K$(x)∇$v$)b(x)·∇$v$). Unlike the standard VEM, the stabilisation scheme can effificiently avoid nonphysical oscillations. The well-posedness of the problem is also proven and error estimates are provided. Numerical examples show the stability of the method for very large Péclet numbers and its applicability to boundary layer problem.

Yuxia Li, Cong Xie & Xinlong Feng. (2020). Streamline Diffusion Virtual Element Method for Convection-Dominated Diffusion Problems. East Asian Journal on Applied Mathematics. 10 (1). 158-180. doi:10.4208/eajam.231118.240619
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