Free Access
Volume 50, Number 1, January-February 2016
Page(s) 163 - 185
Published online 01 December 2015
  1. M. Ainsworth and J.T. Oden, A posteriori error estimation in finite element analysis. Comput. Methods Appl. Mech. Engrg. 142 (1997) 1–88. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An “empirical interpolation” method: application to efficient reduced-basis discretization of partial differential equations. C. R. Acad. Sci. Paris, Ser. I. 339 (2004) 667–672. [Google Scholar]
  3. P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova and P. Wojtaszczyk, Convergence rates for greedy algorithms in reduced basis methods. SIAM J. Math. Anal. 43 (2011) 1457–1472. [CrossRef] [MathSciNet] [Google Scholar]
  4. P.B. Bochev and M.D. Gunzburger, Finite element methods of least-squares type. SIAM Rev. 40 (1998) 789–837. [CrossRef] [MathSciNet] [Google Scholar]
  5. S. Chaturantabut and D.C. Sorensen, Nonlinear model reduction via Discrete Empirical Interpolation. SIAM J. Sci. Comput. 32 (2010) 2737–2764. [CrossRef] [MathSciNet] [Google Scholar]
  6. W. Dahmen, C. Plesken and G. Welper, Double greedy algorithms: reduced basis methods for transport dominated problems. Math. Model. Numer. Anal. 48 (2013) 623–663. [Google Scholar]
  7. M. Drohmann, B. Haasdonk and M. Ohlberger, Reduced basis approximation for nonlinear parametrized evolution equations based on empirical operator interpolation. SIAM J. Sci. Comput. 34 (2012) 934–969. [Google Scholar]
  8. J.L. Eftang, A.T. Patera and E.M. Rønquist, An “hp” certified reduced basis method for parametrized elliptic partial differential equations. SIAM J. Sci. Comput. 32 (2010) 3170–3200. [CrossRef] [MathSciNet] [Google Scholar]
  9. P. Ladevèze and D. Leguillion, Error estimate procedure in the finite element method and applications. SIAM J. Numer. Anal. 20 (1983) 485–509. [CrossRef] [MathSciNet] [Google Scholar]
  10. P. Ladevèze and L. Chamoin, On the verification of model reduction methods based on the proper generalized decomposition. Comput. Methods Appl. Mech. Engrg. 200 (2011) 2032–2047. [CrossRef] [MathSciNet] [Google Scholar]
  11. Y. Maday and O. Mula, A Generalized Empirical Interpolation Method: Application of Reduced Basis Techniques to Data Assimilation. In Anal. Numer. Partial Differ. Equations, edited by F. Brezzi, P.C. Franzone, U. Gianazza and G. Gilardi. Springer-Verlag (2013) 221–235. [Google Scholar]
  12. W.F. Mitchell, Adaptive refinement for arbitrary finite-element spaces with hierarchical bases. J. Comput. Appl. Math. 36 (1991) 65–78. [CrossRef] [Google Scholar]
  13. P. Morin, R.H. Nochetto and K.G. Siebert, Convergence of adaptive finite element methods. SIAM Rev. 44 (2002) 631–658. [CrossRef] [MathSciNet] [Google Scholar]
  14. A.I. Pehlivanov, G.F. Carey and R.D. Lazarov, Least-squares mixed finite elements for second-order elliptic problems. SIAM J. Numer. Anal. 31 (1994) 1368–1377. [CrossRef] [Google Scholar]
  15. A.I. Pehlivanov, G.F. Carey and P.S. Vassilevski, Least-squares mixed finite element methods for non-selfadjoint elliptic problems: I. Error estimates. Numer. Math. 72 (1996) 501–522. [CrossRef] [MathSciNet] [Google Scholar]
  16. P.A. Raviart and J.M. Thomas, A Mixed Finite Element Method for 2nd Order Elliptic Problems. In Vol. 606 of Lect. Notes Math. Springer-Verlag (1977) 292–315. [Google Scholar]
  17. G. Rozza and K. Veroy, On the stability of the reduced basis method for stokes equations in parametrized domains. Comput. Methods Appl. Mech. Engrg. 196 (2007) 1244–1260. [Google Scholar]
  18. G. Rozza, D.B.P. Huynh and A.T. Patera, 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. 15 (2008) 229–275. [Google Scholar]
  19. A.M. Sauer-Budge, J. Bonet, A. Huerta and J. Peraire, Computing bounds for linear functionals of exact weak solutions to Poisson’s equation. SIAM J. Numer. Anal. 42 (2004) 1610–1630. [CrossRef] [MathSciNet] [Google Scholar]
  20. C. Schwab, p- and hp-Finite Element Methods. Oxford Science Publications, Great Clarendon Street, Oxford, UK (1998). [Google Scholar]
  21. K. Steih and K. Urban, Reduced basis methods based upon adaptive snapshot computations. Preprint arxiv: 1407.1708v1 (2014). [Google Scholar]
  22. T. Tonn, K. Urban and S. Volkwein, Comparison of the reduced-basis and POD a posteriori error estimators for an elliptic linear-quadratic optimal control problem. Math. Comput. Model. Dyn. 17 (2011) 355–369. [CrossRef] [MathSciNet] [Google Scholar]
  23. M. Yano, A reduced basis method with exact-solution certificates for steady symmetric coercive equations. Comput. Methods Appl. Mech. Engrg. 287 (2015) 290–309. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you