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Volume 19, Issue 2-3
Reduced Basis Finite Element Methods for the Korteweg-de Vries-Burgers Equation

Guang-Ri Piao, Fuxia Yao & Wenju Zhao

Int. J. Numer. Anal. Mod., 19 (2022), pp. 369-385.

Published online: 2022-04

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  • Abstract

In this paper, the B-spline Galerkin finite element method and reduced order method for the Korteweg-de Vries-Burgers equation are considered. The semi-discrete and the fully discrete schemes are both provided. The reduced order model of the Korteweg-de Vries-Burgers equation by using proper orthogonal decomposition are provided. The stability and the error estimates of the corresponding schemes are then analyzed. Finally, numerical simulations are presented to show the efficiency of our proposed methods.

  • Keywords

Korteweg-de Vries-Burgers, proper orthogonal decomposition, reduced order modeling, error analysis.

  • AMS Subject Headings

35G61, 65D07, 65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-369, author = {Piao , Guang-RiYao , Fuxia and Zhao , Wenju}, title = {Reduced Basis Finite Element Methods for the Korteweg-de Vries-Burgers Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {2-3}, pages = {369--385}, abstract = {

In this paper, the B-spline Galerkin finite element method and reduced order method for the Korteweg-de Vries-Burgers equation are considered. The semi-discrete and the fully discrete schemes are both provided. The reduced order model of the Korteweg-de Vries-Burgers equation by using proper orthogonal decomposition are provided. The stability and the error estimates of the corresponding schemes are then analyzed. Finally, numerical simulations are presented to show the efficiency of our proposed methods.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20486.html} }
TY - JOUR T1 - Reduced Basis Finite Element Methods for the Korteweg-de Vries-Burgers Equation AU - Piao , Guang-Ri AU - Yao , Fuxia AU - Zhao , Wenju JO - International Journal of Numerical Analysis and Modeling VL - 2-3 SP - 369 EP - 385 PY - 2022 DA - 2022/04 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20486.html KW - Korteweg-de Vries-Burgers, proper orthogonal decomposition, reduced order modeling, error analysis. AB -

In this paper, the B-spline Galerkin finite element method and reduced order method for the Korteweg-de Vries-Burgers equation are considered. The semi-discrete and the fully discrete schemes are both provided. The reduced order model of the Korteweg-de Vries-Burgers equation by using proper orthogonal decomposition are provided. The stability and the error estimates of the corresponding schemes are then analyzed. Finally, numerical simulations are presented to show the efficiency of our proposed methods.

Piao , Guang-RiYao , Fuxia and Zhao , Wenju. (2022). Reduced Basis Finite Element Methods for the Korteweg-de Vries-Burgers Equation. International Journal of Numerical Analysis and Modeling. 19 (2-3). 369-385. doi:
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