A Posteriori Error Analysis for a Dual-mixed FEM for the Darcy-Forchheimer Problem

Abstract

[Abstract]: We consider a dual-mixed variational formulation of the Darcy-Forchheimer model. Assuming that the permeability is a symmetric and positive-definite tensor, we prove the problem is well-posed. For the discretization, we approximate the velocity-pressure pair by Raviart-Thomas elements of the lowest order and piecewise constants, respectively. The corresponding discrete problem is well-posed, and we derive a priori error estimates. We also develop an a posteriori error analysis of the residual type and show the reliability of the new a posteriori error indicator. Finally, we provide some numerical experiments that support the theoretical results and suggest the indicator’s eventual efficiency.