TY - JOUR
T1 - Superconvergence Analysis of Low Order Nonconforming Mixed Finite Element Methods for Time-Dependent Navier-Stokes Equations
AU - Yang , Huaijun
AU - Shi , Dongyang
AU - Liu , Qian
JO - Journal of Computational Mathematics
VL - 1
SP - 63
EP - 80
PY - 2020
DA - 2020/09
SN - 39
DO - http://doi.org/10.4208/jcm.1907-m2018-0263
UR - https://global-sci.org/intro/article_detail/jcm/18278.html
KW - Navier-Stokes equations, Nonconforming MFEM, Supercloseness and superconvergence.
AB - <p style="text-align: justify;">In this paper, the superconvergence properties of the time-dependent Navier-Stokes equations are investigated by a low order nonconforming mixed finite element method (MFEM). In terms of the integral identity technique, the superclose error estimates for both the velocity in broken $H^1$-norm and the pressure in $L^2$-norm are first obtained, which play a key role to bound the numerical solution in $L^{\infty}$-norm. Then the corresponding global superconvergence results are derived through a suitable interpolation postprocessing approach. Finally, some numerical results are provided to demonstrate the theoretical analysis.</p>