Goal-oriented mesh adaptivity for inverse problems in linear micromorphic elasticity. (December 2021) - Ju, X.; Mahnken, R.; Liang, L.; Xu, Y.
Highlights: A compact formulation for micromorphic elasticity that is convenient for an error estimation. An efficient gradient-based solver for the inverse problem based on a sensitivity analysis of generalized constitutive relations. Goal-oriented error estimator derived from a two-level optimization framework. An adaptive mesh refinement algorithm aiming at an error control of a quantity of interest as a user-defined functional of material parameters. Abstract: 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.