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Volume 19, Issue 2
Convergence and Superconvergence of Hermite Bicubic Element for Eigenvalue Problem of the Biharmonic Equation

Dong-Sheng Wu

J. Comp. Math., 19 (2001), pp. 139-142.

Published online: 2001-04

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  • Abstract

In this paper,we discuss the convergence and superconvergence for eigenvalue problem of the biharmonic equation by using the Hermite bicubic element. Based on asymptotic error expansions and interpolation postprocessing, we gain the following estimation: $$0 \le \bar{\lambda}_h - \lambda \le C_\epsilon h^{8-\epsilon}$$ where $\epsilon＞0$ is an arbitrary small positive number and $C_\epsilon ＞0$ is a constant.

  • Keywords

Hermite bicubic element, Biharmonic equation, Interpolation postprocessing, Eigenvalue problem.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-19-139, author = {Wu , Dong-Sheng}, title = {Convergence and Superconvergence of Hermite Bicubic Element for Eigenvalue Problem of the Biharmonic Equation}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {2}, pages = {139--142}, abstract = {

In this paper,we discuss the convergence and superconvergence for eigenvalue problem of the biharmonic equation by using the Hermite bicubic element. Based on asymptotic error expansions and interpolation postprocessing, we gain the following estimation: $$0 \le \bar{\lambda}_h - \lambda \le C_\epsilon h^{8-\epsilon}$$ where $\epsilon＞0$ is an arbitrary small positive number and $C_\epsilon ＞0$ is a constant.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8965.html} }
TY - JOUR T1 - Convergence and Superconvergence of Hermite Bicubic Element for Eigenvalue Problem of the Biharmonic Equation AU - Wu , Dong-Sheng JO - Journal of Computational Mathematics VL - 2 SP - 139 EP - 142 PY - 2001 DA - 2001/04 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8965.html KW - Hermite bicubic element, Biharmonic equation, Interpolation postprocessing, Eigenvalue problem. AB -

In this paper,we discuss the convergence and superconvergence for eigenvalue problem of the biharmonic equation by using the Hermite bicubic element. Based on asymptotic error expansions and interpolation postprocessing, we gain the following estimation: $$0 \le \bar{\lambda}_h - \lambda \le C_\epsilon h^{8-\epsilon}$$ where $\epsilon＞0$ is an arbitrary small positive number and $C_\epsilon ＞0$ is a constant.

Wu , Dong-Sheng. (2001). Convergence and Superconvergence of Hermite Bicubic Element for Eigenvalue Problem of the Biharmonic Equation. Journal of Computational Mathematics. 19 (2). 139-142. doi:
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