TY - JOUR T1 - Superconvergence of the Finite Volume Method for Stokes Problems 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.