A Posterior Error Estimate for an Iterative Scheme Associated to the Darcy-Forchheimer Problem with Pressure Boundary Condition

3e900dfe-46e5-491f-9e65-b9a1ded86d7320251009064230428wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON FLUID MECHANICS2224-347X1790-508710.37394/232013http://wseas.org/wseas/cms.action?id=4036130202513020252010.37394/232013.2025.20https://wseas.com/journals/fluids/2025.phpA Posterior Error Estimate for an Iterative Scheme Associated to the Darcy-Forchheimer Problem with Pressure Boundary ConditionRimAldbaissyFaculty of engineering (ESIB), Saint Joseph University of Beirut, LEBANONToniSayahLaboratoire de Mathématiques et Applications, URMM, CAR, Faculté des Sciences, Université Saint-Joseph de Beyrouth, B.P 11-514 Riad El Solh, Beyrouth 1107 2050, LEBANONThis paper investigates the a posteriori error estimates associated with the Darcy–Forchheimer problem under pressure boundary conditions. The problem is discretized using finite element methods and an iterative scheme is recalled along with its corresponding convergence properties. We then derive a posteriori error estimates, where the error between the exact and approximate solutions is bounded by two types of indicators: one related to the discretization and the other to the iteration process. Finally, we present several numerical experiments using the adaptive mesh method to highlight the effectiveness of the proposed approach.1092025109202511512812https://wseas.com/journals/fluids/2025/a245113-405.pdf10.37394/232013.2025.20.12https://wseas.com/journals/fluids/2025/a245113-405.pdf10.1007/s00211-008-0157-7GIRAULT V., WHEELER M.F., Numerical discretization of a Darcy-Forchheimer model, Numer. Math. 110(2), 161-198 (2008). LOPEZ H., MOLINA B., JOSE J.S., Comparison between different numerical discretizations for a Darcy-Forchheimer model, Electron. Trans. Numer. Anal. 34, 187-203 (2009). 10.1051/m2an/2021066SAYAH T., SEMAAN G., TRIKI F., Finite element methods for the Darcy-Forchheimer problem coupled with the convection-diffusion-reaction problem, ESAIM Math. 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