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Stability, convergence, and accuracy of a new finite element method for the circular arch problem. (English) Zbl 0607.73077
The arch problem with shear deformation based upon the Hellinger-Reissner variational formulation is studied in a parameter-dependent form. A mixed Petrov-Galerkin method is used to construct a discrete approximation. Finite elements with equal-order discontinuous stress and continuous displacement interpolations, unstable in the Galerkin method, are proved to be stable in the new formulation. Error estimates indicate optimal rates of convergence for displacements and suboptimal rates, with gap one, for stresses. Numerical experiments confirm these estimates. The good accuracy of the mixed Petrov-Galerkin method is illustrated in some deep and shallow thin arch examples. No shear or membrane locking is present using full integration schemes.

74S05 Finite element methods applied to problems in solid mechanics
65K10 Numerical optimization and variational techniques
74K15 Membranes
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
Full Text: DOI
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