A posteriori error estimates for the Brinkman-Darcy-Forchheimer problem

TL;DR

This paper develops and analyzes a posteriori error estimates for the Brinkman-Darcy-Forchheimer problem using finite element discretization, providing practical error indicators for adaptive methods.

Contribution

It introduces novel a posteriori error estimators for the Brinkman-Darcy-Forchheimer equations, combining discretization and linearization error indicators.

Findings

Numerical experiments validate the effectiveness of the error estimators.

The proposed indicators accurately reflect the discretization and linearization errors.

The method enhances adaptive finite element strategies for complex flow problems.

Abstract

In this paper, we study the "a posteriori" error estimate corresponding to the Brinkman-Darcy-Forchheimer problem. We introduce the variational formulation discretised by using the finite element method. Then, we establish an "a posteriori" error estimation with two types of error indicators related to the discretization and to the linearization. Finally, numerical investigations are shown and discussed.