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Volume 9, Issue 4
Asymptotic Expansion and Superconvergence for Triangular Linear Finite Element on a Class of Typical Mesh

H. Yu & Y. Huang

Int. J. Numer. Anal. Mod., 9 (2012), pp. 892-906.

Published online: 2012-09

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  • Abstract

In this paper, we present a new approach to obtain the asymptotic expansion and superconvergence for the linear element on Union Jack mesh. First, we construct a generalized interpolation function and its discrete harmonic extension by using the energy embedding method and the method of separation of variables. Then, we present elaborate estimates for the generalized interpolation function and the harmonic extension. Finally, the asymptotic expansion, superconvergence and extrapolation are obtained based on those estimates.

  • Keywords

Finite element, Superconvergence, Asymptotic expansion, Extrapolation, Discrete harmonic extension.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-892, author = {H. Yu and Y. Huang}, title = {Asymptotic Expansion and Superconvergence for Triangular Linear Finite Element on a Class of Typical Mesh}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {4}, pages = {892--906}, abstract = {

In this paper, we present a new approach to obtain the asymptotic expansion and superconvergence for the linear element on Union Jack mesh. First, we construct a generalized interpolation function and its discrete harmonic extension by using the energy embedding method and the method of separation of variables. Then, we present elaborate estimates for the generalized interpolation function and the harmonic extension. Finally, the asymptotic expansion, superconvergence and extrapolation are obtained based on those estimates.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/664.html} }
TY - JOUR T1 - Asymptotic Expansion and Superconvergence for Triangular Linear Finite Element on a Class of Typical Mesh AU - H. Yu & Y. Huang JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 892 EP - 906 PY - 2012 DA - 2012/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/664.html KW - Finite element, Superconvergence, Asymptotic expansion, Extrapolation, Discrete harmonic extension. AB -

In this paper, we present a new approach to obtain the asymptotic expansion and superconvergence for the linear element on Union Jack mesh. First, we construct a generalized interpolation function and its discrete harmonic extension by using the energy embedding method and the method of separation of variables. Then, we present elaborate estimates for the generalized interpolation function and the harmonic extension. Finally, the asymptotic expansion, superconvergence and extrapolation are obtained based on those estimates.

H. Yu and Y. Huang. (2012). Asymptotic Expansion and Superconvergence for Triangular Linear Finite Element on a Class of Typical Mesh. International Journal of Numerical Analysis and Modeling. 9 (4). 892-906. doi:
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