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Equal‐order finite elements with nodal projection stabilization for Darcy–Forchheimer model
Author(s) -
Zhang Xianqiang,
Xu Qiuyan
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22591
Subject(s) - mathematics , finite element method , norm (philosophy) , mathematical analysis , projector , divergence (linguistics) , convergence (economics) , inverse , geometry , physics , linguistics , philosophy , optics , political science , law , economics , thermodynamics , economic growth
In this paper, we propose and analyze a stabilized mixed finite element method based on a local Scott–Zhang projector for Darcy–Forchheimer model, using continuous equal‐order finite elements for the velocity and pressure. This type of method belongs to the class of symmetric stabilization techniques, which provides additional control over the fluctuations of the velocity divergence and pressure gradient. An optimal error estimate in the H (div)‐norm for the velocity and quasi‐optimal error estimates in the L 2 ‐norm for the velocity and pressure are derived. Numerical experiments are performed to demonstrate the convergence properties of the method.