In this work, we extend goal-oriented mesh adaptivity to parameter identification for a class of linear micromorphic elasticity problems. Starting from a compact formulation in our previous work (Ju and Mahnkhen, 2017), we propose a two-level optimization framework based on goal-oriented error estimation. By means of a sensitivity analysis of the generalized constitutive relations, we establish a gradient-based solver for the inverse problem, where parameters are optimized within an inner optimization loop for a given mesh. Exact error representations are derived from a Lagrange method, aiming at a quantity of interest as a user-defined functional of the parameters. By using a patch recovery technique for enhanced solutions, a computable error estimator is presented and used to drive an adaptive refinement algorithm, which forms an outer optimization loop. For a numerical study, we investigate the performance of the resulting adaptive procedure in case of perfect, incomplete and perturbed data. The results confirm the effectiveness of the proposed adaptive procedure.

在这项工作中，我们将面向目标的网格自适应扩展到一类线性微形弹性问题的参数识别。从我们之前工作（Ju 和 Mahnkhen，2017）中的紧凑公式开始，我们提出了一个基于面向目标的误差估计的两级优化框架。通过对广义本构关系的敏感性分析，我们为逆问题建立了一个基于梯度的求解器，其中参数在给定网格的内部优化循环内进行优化。精确的误差表示源自拉格朗日方法，旨在将感兴趣的数量作为用户定义的参数函数。通过将补丁恢复技术用于增强解决方案，提出了一个可计算的误差估计器，并用于驱动自适应细化算法，这形成了一个外部优化循环。对于数值研究，我们研究了在完美、不完整和扰动数据的情况下生成的自适应程序的性能。结果证实了所提出的自适应程序的有效性。