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A posteriori error estimation for numerical model reduction in computational homogenization of porous media
Author(s) -
Ekre Fredrik,
Larsson Fredrik,
Runesson Kenneth,
Jänicke Ralf
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6504
Subject(s) - estimator , homogenization (climate) , microscale chemistry , mathematics , a priori and a posteriori , proper orthogonal decomposition , norm (philosophy) , mathematical optimization , point of delivery , statistics , biodiversity , ecology , philosophy , mathematics education , epistemology , political science , law , agronomy , biology
Summary Numerical model reduction is adopted for solving the microscale problem that arizes from computational homogenization of a model problem of porous media with displacement and pressure as unknown fields. A reduced basis is obtained for the pressure field using (i) spectral decomposition (SD) and (ii) proper orthogonal decomposition (POD). This strategy has been used in previous work—the main contribution of this article is the extension with an a posteriori estimator for assessing the error in (i) energy norm and in (ii) a given quantity of interest. The error estimator builds on previous work by the authors; the novelty presented in this article is the generalization of the estimator to a coupled problem, and, more importantly, to accommodate the estimator for a POD basis rather than the SD basis. Guaranteed, fully computable and low‐cost bounds are derived and the performance of the error estimates is demonstrated via numerical results.