Harbrecht, Helmut and Karnaev, Viacheslav and Schmidlin, Marc. (2023) Quantifying domain uncertainty in linear elasticity. Preprints Fachbereich Mathematik, 2023 (06).

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Abstract
The present article considers the quantification of uncertainty for the equations of linear elasticity on random domains. To this end, we model the random domains as the images of some given fixed, nominal domain under random domain mappings, which are defined by a KarhunenLoève expansion. We then prove the analytic regularity of the random solution with respect to the countable random input parameters which enter the problem through the KarhunenLoève expansion of the random domain mappings. In particular, we provide appropriate bounds on arbitrary derivatives of the random solution with respect to those input parameters, which enable the use of stateoftheart quadrature methods to compute deterministic statistics such as the mean and variance of quantities of interest such as the random solution itself or the random von Mises stress as integrals over the countable random input parameters in a dimensionally robust way. Numerical examples qualify and quantify the theoretical findings.
Faculties and Departments:  05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht) 12 Special Collections > Preprints Fachbereich Mathematik 

UniBasel Contributors:  Harbrecht, Helmut and Karnaev, Viacheslav and Schmidlin, Marc 
Item Type:  Preprint 
Publisher:  Universität Basel 
Language:  English 
edoc DOI:  
Last Modified:  19 Jun 2023 08:09 
Deposited On:  11 Jun 2023 08:18 
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