TY - JOUR
T1 - A New Error Analysis of Nonconforming $EQ^{rot}_1$ FEM for Nonlinear BBM Equation
AU - Shi , Yanhua
AU - Zhao , Yanmin
AU - Wang , Fenling
AU - Shi , Dongyang
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1227
EP - 1246
PY - 2018
DA - 2018/07
SN - 10
DO - http://doi.org/10.4208/aamm.OA-2017-0264
UR - https://global-sci.org/intro/article_detail/aamm/12596.html
KW - 
AB - <p style="text-align: justify;">Nonconforming $EQ^{rot}_1$ element is applied to solving a kind of nonlinear
Benjamin-Bona-Mahony (BBM for short) equation both for space-discrete and fully
discrete schemes. A new important estimate is proved, which improves the result of
previous works with the exact solution $u$&nbsp;belonging to $H^2(Ω)$ instead of $H^3(Ω)$. And
then, the supercloseness and global superconvergence estimates in broken $H^1$ norm
are obtained for space-discrete scheme. Further, the superclose estimates are deduced
for backward Euler and Crank-Nicolson schemes. To confirm our theoretical analysis,
numerical experiments for backward Euler scheme are executed. It seems that the results
presented herein have never been seen for nonconforming FEMs in the existing
literature.</p>