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On some three-dimensional finite elements for incompressible media. (English) Zbl 0684.73036

An error analysis for some three-dimensional mixed finite element methods for incompressible elasticity and incompressible viscous flow is presented. A continuous pressure approximation leads to a smaller system of linear equations to be solved and is thus advantageous, especially for three-dimensional systems where iterative techniques are employed for solving finite element equations. The three-dimensional analysis in case of tetrahedral elements corresponds to two-dimensional analysis. The analysis for hexahedral elements is, however, more complicated.
Reviewer: V.K.Arya

MSC:

74S05 Finite element methods applied to problems in solid mechanics
76M99 Basic methods in fluid mechanics
76D99 Incompressible viscous fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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