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Nonlinear Galerkin method and two‐step method for the Navier‐Stokes equations
Author(s) -
Yinnian He,
Kaitai Li
Publication year - 1996
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/(sici)1098-2426(199605)12:3<283::aid-num1>3.0.co;2-k
Subject(s) - galerkin method , discretization , mathematics , nonlinear system , discontinuous galerkin method , scheme (mathematics) , convergence (economics) , finite element method , mathematical analysis , navier–stokes equations , physics , quantum mechanics , economics , thermodynamics , economic growth , compressibility
This article represents a new nonlinear Galerkin scheme for the Navier‐Stokes equations. This scheme consists of a nonlinear Galerkin finite element method and a two‐step difference method. Moreover, we also provide a Galerkin scheme. By convergence analysis, two numerical schemes have the same second‐order convergence accuracy for the spatial discretization and time discretization if H is chosen such that H = O ( h 2/3 ). However, the nonlinear Galerkin scheme is simpler than the Galerkin scheme, namely, this scheme can save a large amount of computational time. © 1996 John Wiley & Sons, Inc.