TY - JOUR
T1 - Superconvergence Error Estimate of the Bilinear-Constant Scheme for the Stokes Equations with Damping
AU - Yang , Huaijun
AU - Wang , Lele
AU - Liao , Xin
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1502
EP - 1518
PY - 2024
DA - 2024/10
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2022-0182
UR - https://global-sci.org/intro/article_detail/aamm/23476.html
KW - Stokes equations with damping, bilinear-constant scheme, superclose and superconvergence estimates.
AB - <p style="text-align: justify;">In this paper, the superconvergence error estimate of a low-order conforming mixed finite element scheme, which is called bilinear-constant scheme, for the
Stokes equations with damping is established. In terms of the integral identity technique and dealing with the damping term carefully, the superclose estimates between
the interpolation of the exact solution and the finite element solution for the velocity
in $H^1$-norm and the pressure in $L^2$-norm are first derived. Then, the global superconvergence results for the velocity in $H^1$-norm and the pressure in $L^2$-norm are derived
by a simple postprocessing technique with an economical workload. Finally, some numerical results are presented to demonstrate the correctness of the theoretical analysis.</p>