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A Posteriori Error Estimates for Darcy–Forchheimer’s Problem

  • Toni Sayah , Georges Semaan and Faouzi Triki ORCID logo EMAIL logo
Published/Copyright: November 11, 2022

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.

MSC 2010: 65N30; 65N15; 65J15

Award Identifier / Grant number: ANR-17-CE40-0029

Funding statement: Faouzi Triki was supported by the grant ANR-17-CE40-0029 of the French National Research Agency ANR (project MultiOnde.

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Received: 2022-02-25
Revised: 2022-09-26
Accepted: 2022-10-03
Published Online: 2022-11-11
Published in Print: 2023-04-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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