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

Cunyun Nie, Shi Shu, Haiyuan Yu & Juan Wu

DOI: 10.4208/nmtma.2013.1127nm

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 = {Cunyun Nie, Shi Shu, Haiyuan Yu and Juan Wu}, 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 AU - Cunyun Nie, Shi Shu, Haiyuan Yu & Juan Wu 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 and Juan Wu. (2013). 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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