A posteriori error estimation for numerical model reduction in computational homogenization of porous media. (English) Zbl 07864079
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.
{© 2020 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.}
{© 2020 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.}
MSC:
| 65Nxx | Numerical methods for partial differential equations, boundary value problems |
| 74Qxx | Homogenization, determination of effective properties in solid mechanics |
| 74Sxx | Numerical and other methods in solid mechanics |
Software:
GmshReferences:
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