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Volume 19, Issue 1
Convergence of an Explicit Upwind Finite Element Method to Multi-Dimensional Conservation Laws

Jin-Chao Xu & Lung-An Ying

J. Comp. Math., 19 (2001), pp. 87-100.

Published online: 2001-02

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  • Abstract

An explicit upwind finite element method is given for the numerical computation to multi-dimensional scalar conservation laws. It is proved that this scheme is consistent to the equation and monotone, and the approximate solution satisfies discrete entropy inequality. To guarantee the limit of approximate solutions to be a measure valued solution, we prove an energy estimate. Then the $L^p$ strong convergence of this scheme is proved.

  • Keywords

Conservation law, Finite element method, Convergence.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{JCM-19-87, author = {Xu , Jin-Chao and Ying , Lung-An}, title = {Convergence of an Explicit Upwind Finite Element Method to Multi-Dimensional Conservation Laws}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {1}, pages = {87--100}, abstract = {

An explicit upwind finite element method is given for the numerical computation to multi-dimensional scalar conservation laws. It is proved that this scheme is consistent to the equation and monotone, and the approximate solution satisfies discrete entropy inequality. To guarantee the limit of approximate solutions to be a measure valued solution, we prove an energy estimate. Then the $L^p$ strong convergence of this scheme is proved.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8960.html} }
TY - JOUR T1 - Convergence of an Explicit Upwind Finite Element Method to Multi-Dimensional Conservation Laws AU - Xu , Jin-Chao AU - Ying , Lung-An JO - Journal of Computational Mathematics VL - 1 SP - 87 EP - 100 PY - 2001 DA - 2001/02 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8960.html KW - Conservation law, Finite element method, Convergence. AB -

An explicit upwind finite element method is given for the numerical computation to multi-dimensional scalar conservation laws. It is proved that this scheme is consistent to the equation and monotone, and the approximate solution satisfies discrete entropy inequality. To guarantee the limit of approximate solutions to be a measure valued solution, we prove an energy estimate. Then the $L^p$ strong convergence of this scheme is proved.

Jin-Chao Xu & Lung-An Ying. (1970). Convergence of an Explicit Upwind Finite Element Method to Multi-Dimensional Conservation Laws. Journal of Computational Mathematics. 19 (1). 87-100. doi:
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