# Study of a finite volume - finite element scheme for a nuclear transport model

## TL;DR

This paper develops and analyzes a finite volume - finite element scheme for a complex, nonlinear, coupled model of nuclear waste contamination that includes thermal effects, proving its stability and convergence.

## Contribution

It introduces a novel combined finite volume and finite element scheme for nonlinear coupled convection-diffusion and Darcy equations with proven stability and error estimates.

## Key findings

- Scheme is stable under certain conditions.
- Convergence and error estimates are established.
- Applicable to nonlinear, coupled thermal and contaminant transport models.

## Abstract

We consider a problem of nuclear waste contamination. It takes into account the thermal effects. The temperature and the contaminant's concentration fulfill convection-diffusion-reaction equations. The velocity and the pressure in the flow satisfy the Darcy equation, with a viscosity depending on both concentration and temperature. The equations are nonlinear and strongly coupled. Using both finite volume and nonconforming finite element methods, we introduce a scheme adapted to this problem. We prove the stability and convergence of this scheme and give some error estimates.