Dual hybrid methods for the elasticity and the Stokes problems: A unified approach. (English) Zbl 0880.73064

Farhloul, Mohamed; Fortin, Michel

Numer. Math. 76, No. 4, 419-440 (1997).

Summary: We give a unified approach to construct finite elements based on a dual hybrid formulaton of the linear elasticity problem. In this formulation the stress tensor is considered, but its symmetry is relaxed by a Lagrange multiplier which is nothing else than the rotation. This construction is linked to the approximations of the Stokes problem in the primitive variables, and it leads to a new interpretation of known elements and to new finite elements. Moreover, all estimates are valid uniformly with respect to compressibility and apply in the incompressible case which is close to the Stokes problem.

MSC:

74S05	Finite element methods applied to problems in solid mechanics
74B05	Classical linear elasticity
76D07	Stokes and related (Oseen, etc.) flows

Keywords:

stress tensor; symmetry; Lagrange multiplier; primitive variables; compressibility