# First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: model derivation and realizability theory

## TL;DR

This paper introduces new moment models for linear kinetic equations using finite element and discontinuous-Galerkin methods, demonstrating improved efficiency over classical models especially with non-smooth solutions.

## Contribution

The paper develops two novel classes of moment models based on finite element and discontinuous-Galerkin methods, including realizability conditions and property analysis.

## Key findings

- Models are more efficient than classical full-moment models in non-smooth cases.
- Numerical tests confirm the effectiveness of the new models.
- Realizability conditions are thoroughly investigated.

## Abstract

We provide two new classes of moment models for linear kinetic equations in slab and three-dimensional geometry. They are based on classical finite elements and low-order discontinuous-Galerkin approximations on the unit sphere. We investigate their realizability conditions and other basic properties. Numerical tests show that these models are more efficient than classical full-moment models in a space-homogeneous test, when the analytical solution is not smooth.