A Posteriori Model Error Analysis of 3D-1D Coupled PDEs

The objective of this work is to extend the model reduction technique for coupled 3D-1D elliptic PDEs, previously proposed by the authors, with an a posteriori analysis of the model error, defined as the difference between the solutions of the reference and reduced problem. More precisely, we introduce an estimator for a user-defined functional of the error, computed using a duality approach. This result is particularly useful since it allows to localize the model error on the computational mesh and to investigate the reliability of the model reduction approach.