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A posteriori estimation and adaptive control of the error in the quantity of interest. I: A posteriori estimation of the error in the von Mises stress and the stress intensity factor. (English) Zbl 0973.74083

From the summary: We address the problem of a posteriori error estimation for an engineering quantity of interest which is computed from a finite element solution. As an example, we consider the plane elasticity problem with the von Mises stress and stress intensity factor, as the quantities of interest. The estimates of error in von Mises stress at a point are obtained by partitioning the error into two components with respect to the element which includes the point, the local and the pollution errors, and by constructing separate estimates for each component. The estimates of the error in the stress intensity factors are constructed by employing an extraction method. We demonstrate that our approach gives accurate estimates for rather coarse meshes and elements of various degrees.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74G70 Stress concentrations, singularities in solid mechanics
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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