Error Analysis and Adaptive Methods of Least Squares Nonconforming Finite Element for the Transport Equations (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we consider a least squares nonconforming finite element oflow order for solving the transport equations. We give a detailed overview on the stabilityand the convergence properties of our considered methods in the stability norm.Moreover, we derive residual type a posteriori error estimates for the least squaresnonconforming finite element methods under $H^{−1}$-norm, which can be used as the errorindicators to guide the mesh refinement procedure in the adaptive finite elementmethod. The theoretical results are supported by a series of numerical experiments.