Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 398-412.
Published online: 2018-11
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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} }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.