Abstract
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.
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Laurino, F., Brambilla, S., Zunino, P. (2021). A Posteriori Model Error Analysis of 3D-1D Coupled PDEs. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_65
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DOI: https://doi.org/10.1007/978-3-030-55874-1_65
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