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Conforming finite element methods for incompressible and nearly incompressible continua. (English) Zbl 0582.76028
Large-scale computations in fluid mechanics, Proc. 15th AMS-SIAM Summer Semin. Appl. Math., La Jolla/Calif. 1983, Lect. Appl. Math. 22, Pt. 2, 221-244 (1985).
[For the entire collection see Zbl 0565.00014.]
We shall be interested here in finite element discretizations of problems involving an incompressibility condition. As model problems we consider the Stokes equations for the flow of a viscous, incompressible fluid and the equations of linear plane-strain elasticity for the deformation of an isotropic, nearly incompressible solid. In both cases the incompressibility condition takes the form of a divergence constraint. The finite element methods we study have the property that the approximations to the velocities, respectively to the displacements, are continuous; such methods are generally referred to as conforming.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76M99 Basic methods in fluid mechanics