A posteriori estimation and adaptive control of the error in the quantity of interest. Part I: A posteriori estimation of the error in the von Mises stress and the stress intensity factor
In this paper we address the problem of a posteriori estimation of the error in 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 the stress intensity factor, as the quantities of...
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| Veröffentlicht in: | Computer methods in applied mechanics and engineering 2000-01, Vol.181 (1), p.261-294 |
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| container_title | Computer methods in applied mechanics and engineering |
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| creator | Strouboulis, T. Babuŝka, I. Datta, D.K. Copps, K. Gangaraj, S.K. |
| description | In this paper we address the problem of a posteriori estimation of the error in 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 the stress intensity factor, as the quantities of interest. The estimates of the error in the 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. In Part II we will address the problem of the adaptive control of the error in the quantity of interest (the
goal of the computation), and the construction of goal-adaptive meshes for one or multiple goals. |
| doi_str_mv | 10.1016/S0045-7825(99)00077-8 |
| format | Article |
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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. In Part II we will address the problem of the adaptive control of the error in the quantity of interest (the
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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. In Part II we will address the problem of the adaptive control of the error in the quantity of interest (the
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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. In Part II we will address the problem of the adaptive control of the error in the quantity of interest (the
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| subjects | Computational techniques Exact sciences and technology Finite-element and galerkin methods Fundamental areas of phenomenology (including applications) Mathematical methods in physics Physics Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics |
| title | A posteriori estimation and adaptive control of the error in the quantity of interest. Part I: A posteriori estimation of the error in the von Mises stress and the stress intensity factor |
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