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Approximation of Navier–Stokes incompressible flow using a spectral element method with a local discretization in spectral space
Author(s) -
Black Kelly
Publication year - 1997
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(199711)13:6<587::aid-num1>3.0.co;2-n
Subject(s) - mathematics , spectral element method , discretization , mathematical analysis , stokes flow , spectral method , flow (mathematics) , quadrilateral , partial differential equation , compressibility , space (punctuation) , finite element method , geometry , mixed finite element method , physics , mechanics , linguistics , philosophy , thermodynamics
A spectral element technique is examined, which builds upon a local discretization within the spectral space. To approximate a given system of equations the domain is subdivided into nonoverlapping quadrilateral elements, and within each element a discretization is found in the spectral space. The difference is that the test functions are divided into the higher‐order polynomials, which have zero boundaries and lower‐order polynomials, which are nonzero on one boundary. The method is examined for Navier–Stokes incompressible flow for fluid flow within a driven cavity and for flow over a backstep. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 587–599, 1997