# Analysis of backward Euler/Spectral discretization for an evolutionary mass and heat transfer in porous medium

## TL;DR

This paper analyzes the numerical solution of coupled mass and heat transfer equations in porous media using backward Euler and spectral discretization, establishing theoretical properties and validating with numerical tests.

## Contribution

It provides a rigorous analysis of existence, uniqueness, and stability of solutions for a coupled nonlinear system using spectral methods.

## Key findings

- Existence and uniqueness of solutions are proven.
- Optimal a priori estimates are derived.
- Numerical tests confirm theoretical results.

## Abstract

This paper presents the unsteady Darcy's equations coupled with two nonlinear reaction-diffusion equations, namely this system describes the mass concentration and heat transfer in porous media. The existence and uniqueness of the solution are established for both the variational formulation problem and for its discrete one obtained using spectral discretization. Optimal a priori estimates are given using the Brezzi-Rappaz-Raviart theorem. We conclude by some numerical tests which are in agreement with our theoretical results.