Convergence analysis of numerical schemes for the Darcy-Forchheimer problem

TL;DR

This paper analyzes the convergence of finite element-based iterative schemes for solving the Darcy-Forchheimer problem under different boundary conditions, providing theoretical proofs and numerical validation.

Contribution

It introduces two new iterative schemes for discretized Darcy-Forchheimer equations and proves their well-posedness and convergence.

Findings

Numerical experiments confirm the effectiveness of the proposed schemes.

Theoretical convergence proofs ensure reliability of the methods.

The schemes perform well under various boundary conditions.

Abstract

This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness and the convergence of the corresponding iterative problems are then proven. Finally, several numerical experiments are performed to validate the proposed numerical schemes.