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Approximation of the arch problem by residual-free bubbles. (English) Zbl 1007.74070
Summary: We consider a general loaded arch problem with a small thickness. To approximate the solution of this problem, we develop a conforming Galerkin mixed finite element method which takes into account an approximation of middle line of the arch. But for a very small thickness such a method gives poor error bounds. The conforming Galerkin method is then enriched with residual-free bubble functions.
MSC:
74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
65N15 Error bounds for boundary value problems involving PDEs
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