Spectral discretization of Darcy's equations coupled with the heat equation
Christine Bernardi, Sarra Maarouf, Driss Yakoubi · IMA Journal of Numerical Analysis · 2015
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.