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.