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 -

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.