Volume 6, Issue 2
Superconvergence and Asymptotic Expansions for Bilinear Finite Volume Element Approximations

Cunyun Nie, Shi Shu, Haiyuan Yu & Juan Wu

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 408-423.

Published online: 2013-06

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  • Abstract

Aiming at the isoparametric bilinear finite volume element scheme, we initially derive an asymptotic expansion and a high accuracy  combination formula of the derivatives in the sense of pointwise by employing the energy-embedded method on uniform grids. Furthermore, we prove that the approximate derivatives are convergent of order two. Finally, numerical examples verify the theoretical results.

  • Keywords

Isoparametric bilinear finite volume element scheme, asymptotic expansion, high accuracy combination formula, superconvergence.

  • AMS Subject Headings

65M10, 65M08, 41A60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-6-408, author = {}, title = {Superconvergence and Asymptotic Expansions for Bilinear Finite Volume Element Approximations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {2}, pages = {408--423}, abstract = {

Aiming at the isoparametric bilinear finite volume element scheme, we initially derive an asymptotic expansion and a high accuracy  combination formula of the derivatives in the sense of pointwise by employing the energy-embedded method on uniform grids. Furthermore, we prove that the approximate derivatives are convergent of order two. Finally, numerical examples verify the theoretical results.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.1127nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5911.html} }
TY - JOUR T1 - Superconvergence and Asymptotic Expansions for Bilinear Finite Volume Element Approximations JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 408 EP - 423 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.1127nm UR - https://global-sci.org/intro/article_detail/nmtma/5911.html KW - Isoparametric bilinear finite volume element scheme, asymptotic expansion, high accuracy combination formula, superconvergence. AB -

Aiming at the isoparametric bilinear finite volume element scheme, we initially derive an asymptotic expansion and a high accuracy  combination formula of the derivatives in the sense of pointwise by employing the energy-embedded method on uniform grids. Furthermore, we prove that the approximate derivatives are convergent of order two. Finally, numerical examples verify the theoretical results.

Cunyun Nie, Shi Shu, Haiyuan Yu & Juan Wu. (2020). Superconvergence and Asymptotic Expansions for Bilinear Finite Volume Element Approximations. Numerical Mathematics: Theory, Methods and Applications. 6 (2). 408-423. doi:10.4208/nmtma.2013.1127nm
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