Superconvergence analysis of lower order anisotropic finite element

Guo Qing Zhu; Dong Yang Shi; Shao Chun Chen

doi:10.1007/s10483-007-0814-x

Superconvergence analysis of lower order anisotropic finite element

Guo Qing Zhu^*, Dong Yang Shi, Shao Chun Chen

^*Corresponding author for this work

Zhengzhou University

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

The convergence analysis of the lower order nonconforming element proposed by Park and Sheen is applied to the second-order elliptic problem under anisotropic meshes. The corresponding error estimation is obtained. Moreover, by using the interpolation postprocessing technique, a global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is derived. Numerical results are also given to verify the theoretical analysis.

Original language	English
Pages (from-to)	1119-1130
Number of pages	12
Journal	Applied Mathematics and Mechanics (English Edition)
Volume	28
Issue number	8
DOIs	https://doi.org/10.1007/s10483-007-0814-x
Publication status	Published - Aug 2007
Externally published	Yes

Keywords

Anisotropic
Error estimate
Interpolation postprocessing
Nonconforming finite element
Superconvergence

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10.1007/s10483-007-0814-x

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Zhu, G. Q., Shi, D. Y., & Chen, S. C. (2007). Superconvergence analysis of lower order anisotropic finite element. Applied Mathematics and Mechanics (English Edition), 28(8), 1119-1130. https://doi.org/10.1007/s10483-007-0814-x

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AB - The convergence analysis of the lower order nonconforming element proposed by Park and Sheen is applied to the second-order elliptic problem under anisotropic meshes. The corresponding error estimation is obtained. Moreover, by using the interpolation postprocessing technique, a global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is derived. Numerical results are also given to verify the theoretical analysis.

KW - Anisotropic

KW - Error estimate

KW - Interpolation postprocessing

KW - Nonconforming finite element

KW - Superconvergence

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Superconvergence analysis of lower order anisotropic finite element

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Keywords

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