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Stabilized mixed finite element methods for the Navier‐Stokes equations with damping
Author(s) -
Li Zhenzhen,
Shi Dongyang,
Li Minghao
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5365
Subject(s) - mathematics , uniqueness , norm (philosophy) , finite element method , mathematical analysis , mixed finite element method , numerical analysis , element (criminal law) , political science , law , physics , thermodynamics
In this paper, the stabilized mixed finite element methods are presented for the Navier‐Stokes equations with damping. The existence and uniqueness of the weak solutions are proven by use of the Brouwer fixed‐point theorem. Then, optimal error estimates for the H 1 ‐norm and L 2 ‐norm of the velocity and the L 2 ‐norm of the pressure are derived. Moreover, on the basis of the optimal L 2 ‐norm error estimate of the velocity, a stabilized two‐step method is proposed, which is more efficient than the usual stabilized methods. Finally, two numerical examples are implemented to confirm the theoretical analysis.