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

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.