A new error bound for reduced basis approximation of parabolic partial differential equations

Comptes Rendus Mathematique

Volumn 350, Issue 3-4, 2012, Pages 203-207

  Urban, Karsten ^a   Patera, Anthony T ^b  

^a UNIVERSITY OF ULM   (Germany)

^b Massachusetts Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84857649056     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2012.01.026     Document Type: Article

References (8)

1. Grepl M., Patera A.T. A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. M2AN Math. Model. Numer. Anal. 2005, 39(1):157-181.
2. Haasdonk B., Ohlberger M. Reduced basis method for finite volume approximations of parametrized linear evolution equations. M2AN Math. Model. Numer. Anal. 2008, 42:277-302.
3. Knezevic D.J., Nguyen N.C., Patera A.T. Reduced basis approximation and a posteriori error estimation for the parametrized unsteady Boussinesq equations. Math. Models Methods Appl. Sci. 2011, 21(7):1415-1442.
4. Rovas D.V., Machiels L., Maday Y. Reduced-basis output bound methods for parabolic problems. IMA J. Numer. Anal. 2006, 26(3):423-445.
5. Rozza G., Huynh D.B.P., Patera A.T. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations - Application to transport and continuum mechanics. Arch. Comput. Methods Eng. 2008, 15(3):229-275.
6. Schwab C., Stevenson R. Space-time adaptive wavelet methods for parabolic evolution problems. Math. Comp. 2009, 78:1293-1318.
7. K. Steih, K. Urban, Space-time reduced basis methods for time-periodic parabolic problems, University of Ulm, Preprint, 2012, http://www.uni-ulm.de/mawi/fakultaet/forschung/preprint-server.html.
8. S. Vallaghé, A. Le-Hyaric, M. Fouquemberg, C. Prud'homme, A successive constraint method with minimal offline constraints for lower bounds of parametric coercivity constant, Preprint, hal-00609212, http://hal.archives-ouvertes.fr.