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On the finite element approximation of incompressible flows of an electrically conducting fluid
Author(s) -
Peterson Janet S.
Publication year - 1988
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.1690040105
Subject(s) - finite element method , uniqueness , compressibility , mathematics , weak solution , magnetic field , mathematical analysis , element (criminal law) , pressure correction method , mixed finite element method , weak formulation , incompressible flow , mechanics , physics , boundary value problem , quantum mechanics , political science , law , thermodynamics
We consider the finite element approximation of incompressible flows field of an electrically conducing fluid in the presence of a magnetic where it is assumed that this field is prescribed. A weak form is chosen that is similar in some respects to a weak form used by many authors for the Navier‐Stokes equations. Existence and uniqueness results are presented for the weak problem. A finite element Algorithm is given for the approximate solution of the weak problem and error estimates are derived.