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A locally conservative, discontinuous least‐squares finite element method for the Stokes equations
Author(s) -
Bochev Pavel,
Lai James,
Olson Luke
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2536
Subject(s) - finite element method , stream function , mathematics , divergence (linguistics) , conservation of mass , mathematical analysis , function (biology) , vector field , mixed finite element method , navier–stokes equations , least squares function approximation , extended finite element method , compressibility , moving least squares , geometry , physics , vorticity , mechanics , vortex , linguistics , philosophy , statistics , evolutionary biology , biology , estimator , thermodynamics
Abstract Conventional least‐squares finite element methods (LSFEMs) for incompressible flows conserve mass only approximately. For some problems, mass loss levels are large and result in unphysical solutions. In this paper we formulate a new, locally conservative LSFEM for the Stokes equations wherein a discrete velocity field is computed that is point‐wise divergence free on each element. The central idea is to allow discontinuous velocity approximations and then to define the velocity field on each element using a local stream‐function. The effect of the new LSFEM approach on improved local and global mass conservation is compared with a conventional LSFEM for the Stokes equations employing standard C 0 Lagrangian elements. Copyright © 2011 John Wiley & Sons, Ltd.