TY - JOUR
T1 - Error Analysis and Adaptive Methods of Least Squares Nonconforming Finite Element for the Transport Equations
AU - Liu , Huipo
AU - Wang , Shuanghu
AU - Han , Hongbin
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 871
EP - 886
PY - 2018
DA - 2018/05
SN - 8
DO - http://doi.org/10.4208/aamm.2015.m1104
UR - https://global-sci.org/intro/article_detail/aamm/12121.html
KW - Least squares, nonconforming, transport equations, adaptive methods.
AB - <p style="text-align: justify;">In this paper, we consider a least squares nonconforming finite element of
low order for solving the transport equations. We give a detailed overview on the stability
and the convergence properties of our considered methods in the stability norm.
Moreover, we derive residual type a posteriori error estimates for the least squares
nonconforming finite element methods under $H^{−1}$-norm, which can be used as the error
indicators to guide the mesh refinement procedure in the adaptive finite element
method. The theoretical results are supported by a series of numerical experiments.</p>