A-posteriori reduced basis error-estimates for a semi-discrete in space quasilinear parabolic PDE-Reference-Cited by-同舟云学术

A-posteriori reduced basis error-estimates for a semi-discrete in space quasilinear parabolic PDE

Published:2021-07-09 Issue: Volume: Page:
ISSN:0926-6003
Container-title:Computational Optimization and Applications
language:en
Short-container-title:Comput Optim Appl

Author:

Hoppe Fabian^ORCID,Neitzel Ira

Abstract

AbstractWe prove a-posteriori error-estimates for reduced-order modeling of quasilinear parabolic PDEs with non-monotone nonlinearity. We consider the solution of a semi-discrete in space equation as reference, and therefore incorporate reduced basis-, empirical interpolation-, and time-discretization-errors in our consideration. Numerical experiments illustrate our results.

Funder

Deutsche Forschungsgemeinschaft

Rheinische Friedrich-Wilhelms-Universität Bonn

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Mathematics,Control and Optimization

Link

https://link.springer.com/content/pdf/10.1007/s10589-021-00299-y.pdf

Reference65 articles.

1. Ahmad Ali, A., Deckelnick, K., Hinze, M.: Global minima for semilinear optimal control problems. Comput. Optim. Appl. 65(1), 261–288 (2016). https://doi.org/10.1007/s10589-016-9833-1

2. Alla, A., Hinze, M., Kolvenbach, P., Lass, O., Ulbrich, S.: A certified model reduction approach for robust parameter optimization with PDE constraints. Adv. Comput. Math. 45(3), 1221–1250 (2019). https://doi.org/10.1007/s10444-018-9653-1

3. Alla, A., Kutz, J.N.: Nonlinear model order reduction via dynamic mode decomposition. SIAM J. Sci. Comput. 39(5), B778–B796 (2017). https://doi.org/10.1137/16M1059308

4. Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Arch. Num. Softw. 3(100) (2015). https://doi.org/10.11588/ans.2015.100.20553

5. Amann, H.: Maximal regularity for nonautonomous evolution equations. Adv. Nonlinear Stud. 4(4), 417–430 (2004). https://doi.org/10.1515/ans-2004-0404

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