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**Dual adaptive finite element refinement for multiple local quantities in linear elastostatics.**
*(English)*
Zbl 1193.74156

Summary: We summarize how dual analysis techniques can be used to determine upper bounds of the discretization error, both in terms of global and local outputs. We present formulas for the bounds of the error in local outputs, based on the approach proposed by Greenberg in 1948 and we show that the resulting intervals are the same as those previously presented, based on the approach proposed by Washizu in 1953. We then explain how the elemental contributions to these bounds can be used to define an adaptive strategy that considers multiple quantities and we present its application to a simple plane stress problem.

### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74B05 | Classical linear elasticity |

### Keywords:

adaptive refinement; goal-oriented adaptivity; dual analysis; model verification; error bounds### Software:

Gmsh
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\textit{O. J. B. A. Pereira} and \textit{J. P. M. de Almeida}, Int. J. Numer. Methods Eng. 83, No. 3, 347--365 (2010; Zbl 1193.74156)

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### References:

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