  In this work, we present a novel regularized L$_1$ (RL$_1$) finite element
spatial discretization scheme for radiation transport problems. We review the
recently developed least-squares finite element method in nuclear applications.
We then derive an L$_1$ finite element by minimizing the L$_1$ norm of the
transport residual. To ensure the stability on incident boundary, we newly
develop a consistent L$_1$ boundary condition (BC). The numerical tests
demonstrate such a method effectively prevents the oscillations which would
occur to least-squares finite element when discontinuity exists such as void
and absorber. Further, the RL$_1$ method is accurate in problems with
scattering.
