Finite element analysis is a central tool for predicting the mechanical response of auxetic structures. However, frequently occurring stress singularities, typically due to the geometry of the unit cell, degrade convergence [1]. Since most engineering decisions are based on quantities of interest, such as reaction forces or local displacements, local discretisation errors that compromise their accurate prediction pose significant challenges. Adaptive finite element methods offer a systematic way of retaining accuracy through localized mesh refinement. Using so-called goal-oriented error estimates – which predict the error of a predefined quantity of interest and identify areas in which the discretisation must be refined – makes adaptive methods particularly suited for engineering applications. For elasticity, such estimates can be based on stress equilibration, as demonstrated using energy-norm estimates, e.g. in [2, 3]. In this talk, the accuracy as well as the computational efficiency of goal-oriented error estimates for linear elasticity are discussed. While the method itself controls the discretisation errors, even such a sophisticated solution scheme remains contingent on the fidelity of the underlying physical model. Therefore, a final experimental validation of the proposed methodology, based on two experimentally investigated auxetic test specimens, is performed. References: [1] Verfürth, R. (1994). A posteriori error estimation and adaptive mesh-refinement techniques. J. Comput. Appl. Math., Vol. 50, No. 1, p. 67-83. [2] Brodbeck, M. et al. (2024). Adaptive finite element methods based on flux and stress equilibration using FEniCSx. arXiv [3] Brodbeck, M. et al. (2025). Equilibration-Based A Posteriori Error Estimates for Solid Mechanics. PAMM, Vol. 25, No. 4, p. e70045