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On the locking phenomenon for a class of elliptic problems. (English) Zbl 0798.73054
Summary: We study the numerical behaviour of elliptic problems in which a small parameter is involved and an example concerning the computation of elastic arches is analyzed using this mathematical framework. At first, the statements of the problem and its Galerkin approximations are defined and an asymptotic analysis is performed. Then we give general conditions ensuring that a numerical scheme will converge uniformly with respect to the small parameter. Finally we study an example in computation of arches working in linear elasticity conditions. We build a finite element scheme giving a locking behaviour, and another one which does not.

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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