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Volume 10, Issue 4
A Non-Consistent Virtual Element Method for Reaction Diffusion Equations

Fang Feng, Jianguo Huang & Yue Yu

DOI: 10.4208/eajam.150320.110520

East Asian J. Appl. Math., 10 (2020), pp. 786-799.

Published online: 2020-08

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  • Abstract

A simple virtual element method, avoiding the traditional enhancement technique, is used for numerical solution of a reaction-diffusion problem in the lowest order cases $k$ = 1 and 2. Optimal error estimates are established in $H^1$ and $L^2$ norms. Numerical results are consistent with theoretical findings but show that for $k$ ≥ 3 the method is not optimal.

  • Keywords

Virtual element method, reaction-diffusion problem, non-consistent, enhancement technique, error analysis.

  • AMS Subject Headings

65N30, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-10-786, author = {Feng , FangHuang , Jianguo and Yu , Yue}, title = {A Non-Consistent Virtual Element Method for Reaction Diffusion Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {4}, pages = {786--799}, abstract = {

A simple virtual element method, avoiding the traditional enhancement technique, is used for numerical solution of a reaction-diffusion problem in the lowest order cases $k$ = 1 and 2. Optimal error estimates are established in $H^1$ and $L^2$ norms. Numerical results are consistent with theoretical findings but show that for $k$ ≥ 3 the method is not optimal.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.150320.110520}, url = {http://global-sci.org/intro/article_detail/eajam/17961.html} }
TY - JOUR T1 - A Non-Consistent Virtual Element Method for Reaction Diffusion Equations AU - Feng , Fang AU - Huang , Jianguo AU - Yu , Yue JO - East Asian Journal on Applied Mathematics VL - 4 SP - 786 EP - 799 PY - 2020 DA - 2020/08 SN - 10 DO - http://doi.org/10.4208/eajam.150320.110520 UR - https://global-sci.org/intro/article_detail/eajam/17961.html KW - Virtual element method, reaction-diffusion problem, non-consistent, enhancement technique, error analysis. AB -

A simple virtual element method, avoiding the traditional enhancement technique, is used for numerical solution of a reaction-diffusion problem in the lowest order cases $k$ = 1 and 2. Optimal error estimates are established in $H^1$ and $L^2$ norms. Numerical results are consistent with theoretical findings but show that for $k$ ≥ 3 the method is not optimal.

Feng , FangHuang , Jianguo and Yu , Yue. (2020). A Non-Consistent Virtual Element Method for Reaction Diffusion Equations. East Asian Journal on Applied Mathematics. 10 (4). 786-799. doi:10.4208/eajam.150320.110520
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