Numerical Analysis of a Darcy-Forchheimer Model Coupled with the Heat Equation

This paper discusses a novel three field formulation for the Darcy-Forchheimer flow with nonlinear viscosity depending on temperature coupled heat equation. We show unique solvability of variational problem by using; Galerkin method, Brouwer’s fixed point and some compactness properties. propose study in detail finite element approximation. A priori error estimate is then derived convergence obtained. solution technique formulated to solve numerical experiments that validate theoretical findings are presented.