Construction, analysis and implementation of two nodal finite volume schemes for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:math> model for particle transport in 2D

In this paper, we present two new nodal finite volume schemes for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:math> model on arbitrary polygonal meshes in 2D. We show that these schemes are well-defined, conservative and stable, finally we prove their convergence. We also present some numerical results.