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The primal mixed finite element method and the LBB condition
Author(s) -
Robey Thomas H.
Publication year - 1992
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.1690080405
Subject(s) - mathematics , spurious relationship , finite element method , domain decomposition methods , mathematical analysis , displacement (psychology) , matrix (chemical analysis) , mixed finite element method , kinematics , structural engineering , classical mechanics , engineering , psychology , statistics , materials science , composite material , physics , psychotherapist
Abstract Spurious or kinematic modes have posed a major obstacle to the implementation of the mixed finite element method. This research shows that spurious modes resulting from the approximation spaces not satisfying the LBB condition do not prevent a well posed problem. When the LBB condition is not satisfied, the resulting matrix equations are singular. A direct solution method is presented for the efficient solution of the possibly singular equations. Orthogonal flux basis functions are introduced to simplify the problem. Then the solution procedure is based on nested domain decomposition. This solution procedure is shown to be competitive with direct solution methods for the displacement finite element method. Examples are included to demonstrate various aspects of the LBB condition and the solution procedure.