A Posteriori Error Estimates for Darcy–Forchheimer’s Problem-Reference-Cited by-同舟云学术

A Posteriori Error Estimates for Darcy–Forchheimer’s Problem

Published:2022-11-11 Issue:2 Volume:23 Page:517-544
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Sayah Toni¹,Semaan Georges¹,Triki Faouzi²^ORCID

Affiliation:

1. Laboratoire de “Mathématiques et Applications” , Unité de Recherche “Mathématiques et Modélisation”, CAR, Faculté des sciences , Université Saint-Joseph de Beyrouth , Beirut , Lebanon

2. Laboratoire Jean Kuntzmann , UMR CNRS 5224 , Université Grenoble-Alpes , 700 Avenue Centrale, 38401 Saint-Martin-d’Hères , France

Abstract

Abstract This work deals with the a posteriori error estimates for the Darcy–Forchheimer problem. We first introduce the corresponding variational formulation for the nonlinear problem and discretize it by using the finite-element method. We then propose a linear iterative scheme to solve the nonlinear variational problem for a fixed mesh step. Finally, 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. Numerical computations are performed to show the effectiveness of the derived error indicators.

Funder

Agence Nationale de la Recherche

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2022-0047/pdf

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