A posteriori error estimates for Darcy-Forchheimer's problem

TL;DR

This paper develops and analyzes a posteriori error estimates for the Darcy-Forchheimer problem using finite-element discretization, introducing two types of error indicators and validating their effectiveness through numerical experiments.

Contribution

It introduces two computable error indicators for the Darcy-Forchheimer problem and demonstrates their effectiveness via numerical validation.

Findings

Error indicators effectively estimate errors in Darcy-Forchheimer simulations

Numerical results confirm the reliability of the proposed error estimates

The approach improves adaptive finite-element methods for nonlinear flow problems

Abstract

This work deals with the a posteriori error estimates for the Darcy-Forchheimer problem. We introduce the corresponding variational formulation and discretize it by using the finite-element method. A posteriori error estimate with two types of computable error indicators is showed. The first one is linked to the linearization and the second one to the discretization. Finally, numerical computations are performed to show the effectiveness of the error indicators.