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### Extrapolation error estimator

A different error estimator is based on the discontinuities which arise by extrapolating the stress values at the integration points to the nodes. It is triggered by selecting ERR underneath the *EL FILE keyword card.

A node usually belongs to several elements. The stresses are available (and most accurate) at the integration points of these elements. To obtain stress values at the nodes, CalculiX extrapolates the stress tensor at the integration points to the nodes. If a node belongs to n elements, one obtains in this way n different stress tensors at one and the same node. The final stress tensor at the node is obtained by taking the mean of all these stress tensors [16].

If the mesh is fine, the difference between these stress tensors should not be very large. Conversely, large differences may point to inaccurate results. This property is used to obtain an error estimate based on the worst principal stress and the von Mises stress (the worst principal stress is the principal stress the absolute value of which is larger than the absolute value of the other two principal stresses).

The n stress tensors at one and the same node lead to n different worst principal stress values. The standard deviation of these values is stored in PSTD. In the same way the n von Mises stresses can be dealt with: VMSTD is the standard deviation of the Von Mises stresses of all extrapolated stress tensors. PSTD and VMSTD can be considered as an indicator for the size of the error.

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