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In this work, we present a novel regularized L$_1$ (RL$_1$) finite elementspatial discretization scheme for radiation transport problems. We review therecently developed least-squares finite element method in nuclear applications.We then derive an L$_1$ finite element by minimizing the L$_1$ norm of thetransport residual. To ensure the stability on incident boundary, we newlydevelop a consistent L$_1$ boundary condition (BC). The numerical testsdemonstrate such a method effectively prevents the oscillations which wouldoccur to least-squares finite element when discontinuity exists such as voidand absorber. Further, the RL$_1$ method is accurate in problems withscattering.

Effective Non-oscillatory Regularized L$_1$ Finite Elements for Particle Transport Simulations