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A symmetrized vector potential‐vorticity formulation of the Stokes system and its Finite Element Discretization
Author(s) -
Ruas V.,
Trales P.R.
Publication year - 2006
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200510239
Subject(s) - discretization , vorticity , stream function , bounded function , finite element method , domain (mathematical analysis) , mathematics , mathematical analysis , function (biology) , vector valued function , boundary (topology) , vortex , physics , mechanics , evolutionary biology , biology , thermodynamics
The aim of this paper is to study a formulation of the Stokes system in a bounded three‐dimensional domain, expressed in terms of the vorticity and a vector potential, whose gradient is fully prescribed on the boundary of the domain. The formulation is based on an uncoupling technique following principles similar to those exploited by Glowinski & Pironneau [7] in the case of the stream function‐vorticity formulation of the two‐dimensional Stokes system. A solution scheme of the resulting system using special classes of finite elements is given.