A New Stabilised Finite Element Method for the Darcy-Forchheimer Model

Abstract

[Abstract] In this paper, we propose a new stabilised finite element method for the Darcy-Forchheimer model based on the jump stabilisation technique. We prove the well-posedness of the discrete scheme and develop an a priori error analysis. We provide two academic examples that support the theory and study the effect of the Forchheimer number on convergence. Finally, we adapt the method to solve the coupling of the Darcy-Forchheimer model with a heat equation and provide several numerical experiments, including an application to the simulation of wood drying and a three-dimensional example.