A new non-intrusive technique for the construction of admissible stress fields in model verification

In this paper, we investigate a new procedure for constructing admissible stress tensors that are needed in some methods for robust global/goal-oriented error estimation. This procedure is based on properties of the approximate finite element solution which are applied through prolongation conditions. It involves the calculation of equilibrated tractions along element boundaries, leading to the determination of admissible stress tensors at the element level. The main idea of the proposed approach is to use the partition of unity method for the calculation of the equilibrated tractions, thus defining local problems on patches of elements which can be solved in an automatic and non-intrusive manner. Therefore, this hybrid procedure leads to reasonable computational costs and can be easily implemented into existing finite element codes. Two-dimensional experiments illustrate the capabilities of the method as compared to alternative approaches.