Abstract
In this paper assessment of the reliability of the results in the finite element method is studied by using probability theory. A probabilistic error indicator is presented which is based on Kriging error interpolation and is used for mesh smoothing purpose. Effective parameters such as shape functions, volume of elements and distance between nodes are considered simultaneously. The field variation is also considered and is calculated statistically or by other means such as user's sense. This error indicator is used for adaptive mesh smoothing purposes especially in the uncoupled ALE approaches. Robustness and accuracy of the method are shown through several examples on different fields with irregular boundaries or abrupt changes.
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