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Optimal estimates on stabilized finite volume methods for the incompressible Navier–Stokes model in three dimensions
Author(s) -
Li Jian,
Lin Xiaolin,
Zhao Xin
Publication year - 2019
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.22294
Subject(s) - mathematics , finite element method , finite volume method , uniqueness , navier–stokes equations , galerkin method , compressibility , norm (philosophy) , mathematical analysis , discontinuous galerkin method , upper and lower bounds , mechanics , physics , political science , law , thermodynamics
Optimal estimates on stabilized finite volume methods for the three dimensional Navier–Stokes model are investigated and developed in this paper. Based on the global existence theorem [23], we first prove the global bound for the velocity in the H 1 ‐norm in time of a solution for suitably small data, and uniqueness of a suitably small solution by contradiction. Then, a full set of estimates is then obtained by some classical Galerkin techniques based on the relationship between finite element methods and finite volume methods approximated by the lower order finite elements for the three dimensional Navier–Stokes model.