Volume 16, Issue 1
Superconvergence of continuous finite elements with interpolated coefficients for initial value problems of nonlinear ordinary differential equation

Z. Xiong & C. Chen

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 16 (2007), pp. 37-44

Published online: 2007-02

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  • Abstract
The main aim of this paper is to study the approximation to viscoelasticity type equations with a Crouzeix-Raviart type nonconforming finite element on the anisotropic meshes. The superclose property of the exact solution and the optimal error estimate of its derivative with respect to time are derived by using some novel techniques. Moreover, employing a postprocessing technique, the global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is studied.
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@Article{NM-16-37, author = { Z. Xiong and C. Chen}, title = {Superconvergence of continuous finite elements with interpolated coefficients for initial value problems of nonlinear ordinary differential equation}, journal = {Numerical Mathematics, a Journal of Chinese Universities}, year = {2007}, volume = {16}, number = {1}, pages = {37--44}, abstract = { The main aim of this paper is to study the approximation to viscoelasticity type equations with a Crouzeix-Raviart type nonconforming finite element on the anisotropic meshes. The superclose property of the exact solution and the optimal error estimate of its derivative with respect to time are derived by using some novel techniques. Moreover, employing a postprocessing technique, the global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is studied. }, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/8048.html} }
TY - JOUR T1 - Superconvergence of continuous finite elements with interpolated coefficients for initial value problems of nonlinear ordinary differential equation AU - Z. Xiong & C. Chen JO - Numerical Mathematics, a Journal of Chinese Universities VL - 1 SP - 37 EP - 44 PY - 2007 DA - 2007/02 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nm/8048.html KW - AB - The main aim of this paper is to study the approximation to viscoelasticity type equations with a Crouzeix-Raviart type nonconforming finite element on the anisotropic meshes. The superclose property of the exact solution and the optimal error estimate of its derivative with respect to time are derived by using some novel techniques. Moreover, employing a postprocessing technique, the global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is studied.
Z. Xiong and C. Chen. (2007). Superconvergence of continuous finite elements with interpolated coefficients for initial value problems of nonlinear ordinary differential equation. Numerical Mathematics, a Journal of Chinese Universities. 16 (1). 37-44. doi:
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