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Gradient error estimator

A different error estimator is based on the difference between the maximum and minimum first (=maximal) principal stress at the integration points in the elements belonging to one and the same node . 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. If the largest difference between the first principal stress at all integration points within an element is small, the stresses vary little across the element and the element size is deemed adequate to yield an accurate stress prediction. From the absolute value of the largest difference a relative value (called REL in the frd-file; it is obtained by selecting ERR underneath the *EL FILE or *ELEMENT OUTPUT card) is calculated. The relative value is the absolute value divided by the absolute value of the largest first principal stress within the element.

To obtain the relative value at the nodes the maximum is taken across all elements belonging to the node. In a strict sense this is not an error estimator, it is just a measure for the variation of the largest principal stress across all elements belonging to the node.

By applying this concept to a large number of examples for which the stress error was known a heuristic relationship was deduced. It allows, for a given element type, to determine the error in the maximum principal stress in a node (called STR in the frd file; it is obtained by selecting ERR underneath the *EL FILE or *ELEMENT OUTPUT card) from the relative measure just defined (describing the relative change of the largest principal stress in the adjacent elements). If a node belongs to several element types the worst value is taken. The STR-value is in %.

For heat transfer a similar error estimator was coded for the heat flux. It is triggered by selecting HER underneath the *EL FILE keyword card. It represents the variation of the size of the heat flux vector across all elements belonging to one and the same node. For thermal problems no heuristic relationships connecting the largest temperature gradient in the adjacent element to a node and the temperature error in the node has been established. Instead,the user obtains the relative value of the largest different in the temperature gradient in the adjacent elements (HERREL).


next up previous contents
Next: Output variables Up: Error estimators Previous: Zienkiewicz-Zhu error estimator   Contents
guido dhondt 2017-04-02