A posteriori error estimation for numerical model reduction in computational homogenization of porous media. (13th September 2020)

• Record Type: Journal Article
• Authors: Ekre, Fredrik; Larsson, Fredrik; Runesson, Kenneth; Jänicke, Ralf
• Other Names: Giacomini Matteo guestEditor.; Veroy Karen guestEditor.; Díez Pedro guestEditor.
• Is Part Of: International journal for numerical methods in engineering. Volume 121:Number 23(2020)
• Page Start: 5350
• Page End: 5380
• Publication Date: 2020-09-13
• Subjects: computational homogenization -- error control -- model reduction; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6504
• Languages: English
• ISSNs: 0029-5981

Abstract

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.