CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France, Sorbonne Université, UPMC Univ Paris 06, UMR 7598, LJLL, F-75005, Paris, France and Départmente de Mathématiques et Statistiques, Université Laval, Québec, Canada, firstname.lastname@example.org
In this paper, we consider the heat equation coupled with Darcy's law with a nonlinear source term describing heat production due to an exothermic chemical reaction. The existence and uniqueness of a solution are established. Next, a spectral discretization of the problem is presented and thoroughly analysed. Finally, we present some numerical experiments which confirm the interest of the discretization.