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Arnold, Douglas N.; Douglas, Jim jun.; Gupta, Chaitan P.

A family of higher order mixed finite element methods for plane elasticity. (English) Zbl 0558.73066

Numer. Math. 45, 1-22 (1984).
The authors construct a new family of finite elements for the approximation of a mixed variational formulation of linear elasticity (formulation in terms of displacements and stresses). Approximation properties of these elements are studied and estimates of optimal order are derived for both, the displacement and stress field. All estimates are valid for the incompressible case, as well. Elements are the vector analogue of Raviart-Thomas mixed finite elements for the scalar elliptic equation.
Reviewer: J.Haslinger

Cited in 1 Review
Cited in 146 Documents

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S99 Numerical and other methods in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)

Keywords:

new family of finite elements; mixed variational formulation; linear elasticity; displacements; stresses; Approximation properties; estimates of optimal order; incompressible case; analogue of Raviart-Thomas mixed finite elements
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References:

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