The DOI matches its Crossref record; 33 of the 33 references it cites were found in a registry or an index.
On the convergence of generalized polynomial chaos expansions
Open accessAbstract
A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial chaos expansions to the correct limit and complement these with illustrative examples.
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Cites
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Cited by
Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion
Oladyshkin, S., & Nowak, W. (2012) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2012.05.002 · Cited by 451
Uncertainty quantification of simulated biomechanical stimuli in coronary artery bypass grafts
Tran, J. S., Schiavazzi, D. E., Kahn, A. M., & Marsden, A. L. (2019) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2018.10.024 · Cited by 37
Metadata
- Authors
- Ernst, O. G., Mugler, A., Starkloff, H.-J., & Ullmann, E.
- Venue
- ESAIM: Mathematical Modelling and Numerical Analysis
- Publisher
- EDP Sciences
- Published
- 2011-10-12
- Volume
- 46
- Issue
- 2
- Pages
- 317-339
- ISSN
- 0764-583X (ISSN-L)
- 1290-3841
- OpenAlex
- W2150062983
- Cited by
- 414
- References
- 33
- FWCI
- 21.27
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Ernst, O. G., Mugler, A., Starkloff, H.-J., & Ullmann, E. (2012). On the convergence of generalized polynomial chaos expansions. ESAIM: Mathematical Modelling and Numerical Analysis. https://doi.org/10.1051/m2an/2011045
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