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Volume 11, Issue 2
Superconvergence of the Finite Volume Method for Stokes Problems

Tie Zhang & Yongchao Tang

DOI: 10.4208/nmtma.OA-2017-0049

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 398-412.

Published online: 2018-11

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  • Abstract

This paper presents a superconvergence analysis of the finite volume method for Stokes problems using the $P_1$ – $P_1$ velocity-pressure element pair. Based on some superclose estimates on the interpolation function, we derive a superconvergence result of rate $\mathcal{O}(h^{\frac{3}{2}})$ for the post-processed velocity approximation in the $H^1$-norm and for the directly computed pressure approximation in the $L_2$-norm, respectively. Numerical experiments are provided to illustrate the theoretical analysis.

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@Article{NMTMA-11-398, author = {Tie Zhang and Yongchao Tang}, title = {Superconvergence of the Finite Volume Method for Stokes Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {2}, pages = {398--412}, abstract = {

This paper presents a superconvergence analysis of the finite volume method for Stokes problems using the $P_1$ – $P_1$ velocity-pressure element pair. Based on some superclose estimates on the interpolation function, we derive a superconvergence result of rate $\mathcal{O}(h^{\frac{3}{2}})$ for the post-processed velocity approximation in the $H^1$-norm and for the directly computed pressure approximation in the $L_2$-norm, respectively. Numerical experiments are provided to illustrate the theoretical analysis.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0049}, url = {http://global-sci.org/intro/article_detail/nmtma/12436.html} }
TY - JOUR T1 - Superconvergence of the Finite Volume Method for Stokes Problems AU - Tie Zhang & Yongchao Tang JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 398 EP - 412 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.OA-2017-0049 UR - https://global-sci.org/intro/article_detail/nmtma/12436.html KW - AB -

This paper presents a superconvergence analysis of the finite volume method for Stokes problems using the $P_1$ – $P_1$ velocity-pressure element pair. Based on some superclose estimates on the interpolation function, we derive a superconvergence result of rate $\mathcal{O}(h^{\frac{3}{2}})$ for the post-processed velocity approximation in the $H^1$-norm and for the directly computed pressure approximation in the $L_2$-norm, respectively. Numerical experiments are provided to illustrate the theoretical analysis.

Tie Zhang and Yongchao Tang. (2018). Superconvergence of the Finite Volume Method for Stokes Problems. Numerical Mathematics: Theory, Methods and Applications. 11 (2). 398-412. doi:10.4208/nmtma.OA-2017-0049
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