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All issues Volume 48 / No 1 (January-February 2014) ESAIM: M2AN, 48 1 (2014) 259-283 References
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Issue
ESAIM: M2AN
Volume 48, Number 1, January-February 2014
Page(s) 259 - 283
DOI https://doi.org/10.1051/m2an/2013100
Published online 10 January 2014
  1. R.E. Bank and A. Weiser, Some a posteriori error estimators for elliptic partial differential equations. Math. Comput. 44 (1985) 303–320. [CrossRef] [Google Scholar]
  2. M. Barrault, N.C. Nguyen, Y. Maday 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. A. Buffa, Y. Maday, A. Patera, C. Prud’homme and G. Turinici, A priori convergence of the greedy algorithm for the parametrized reduced basis. M2AN 46 (2012) 595–603. Special Issue in honor of David Gottlieb. [Google Scholar]
  5. T. Bui-Thanh, Model-Constrained Optimization Methods for Reduction of Parameterized Large-Scale Systems, MIT Thesis (2007). [Google Scholar]
  6. T. Bui-Thanh, K. Willcox and O. Ghattas, Model reduction for large-scale systems with high-dimensional parametric input space. SIAM J. Sci. Comput. 30 (2008) 3270–3288. [CrossRef] [MathSciNet] [Google Scholar]
  7. Y. Chen, J.S. Hesthaven, Y. Maday and J. Rodriguez, A monotonic evaluation of lower bounds for inf-sup stability constants in the frame of reduced basis approximations. C.R. Acad. Sci. Paris, Ser. I 346 (2008) 1295–1300. [CrossRef] [Google Scholar]
  8. Y. Chen, J.S. Hesthaven, Y. Maday and J. Rodriguez, Improved successive constraint method based a posteriori error estimate for reduced basis approximation of 2d Maxwells problem. ESAIM: M2AN 43 (2009) 1099–1116. [CrossRef] [EDP Sciences] [Google Scholar]
  9. Y. Chen, J.S. Hesthaven, Y. Maday and J. Rodriguez, Certified reduced basis methods and output bounds for the harmonic maxwell equations. SIAM J. Sci. Comput. 32 (2010) 970–996. [CrossRef] [MathSciNet] [Google Scholar]
  10. J.L. Eftang, A.T. Patera and E.M. Ronquist, An “hp” certified reduced basis method for parametrized elliptic partial differential equations. SIAM J. Sci. Comput. 32 (2010) 3170–3200. [CrossRef] [MathSciNet] [Google Scholar]
  11. J.L. Eftang and B. Stamm, Parameter multi-domain hp empirical interpolation. Int. J. Numer. Meth. Engng. 90 (2012) 412–428. [Google Scholar]
  12. B. Fares, J.S. Hesthaven, Y. Maday and B. Stamm, The reduced basis method for the electric field integral equation. J. Comput. Phys. 230 (2011) 5532–5555. [Google Scholar]
  13. M.A. Grepl, Y. Maday, N. C. Nguyen and A.T. Patera, Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. Math. Model. Numer. Anal. 41 (2007) 575–605. [Google Scholar]
  14. M.A. Grepl and A.T. Patera, A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. M2AN 39 (2005) 157–181. [Google Scholar]
  15. B. Haasdonk, M. Dihlmann and M. Ohlberger, A training set and multiple basis functions generation approach for parametrized model reduction based on adaptive grids in parameter space. Math. Comput. Modell. Dyn. Syst. 17 (2011) 423-442. [Google Scholar]
  16. B. Haasdonk and M. Ohlberger, Basis construction for reduced basis methods by adaptive parameter grids, in Proc. International Conference on Adaptive Modeling and Simulation 2007 (2007) 116–119. [Google Scholar]
  17. J.S. Hesthaven and S. Zhang, On the use of ANOVA expansions in reduced basis methods for high-dimensional parametric partial differential equations, Brown Division of Applied Math Scientific Computing Tech Report 2011-31. [Google Scholar]
  18. D.B.P. Huynh, G. Rozza, S. Sen and A.T. Patera, A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants. C.R. Acad. Sci. Paris, Ser. I 345 (2007) 473–478. [Google Scholar]
  19. Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383–404. [CrossRef] [MathSciNet] [Google Scholar]
  20. Y. Maday and B. Stamm, Locally adaptive greedy approximations for anisotropic parameter reduced basis spaces, arXiv: math.NA, Apr 2012, accepted in SIAM Journal on Scientific Computing. [Google Scholar]
  21. A.T. Patera and G. Rozza, Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations, Version 1.0, Copyright MIT 2006, to appear in (tentative rubric) MIT Pappalardo Graduate Monographs in Mechanical Engineering. [Google Scholar]
  22. A. Quarteroni, G. Rozza and A. Manzoni, Certified reduced basis approximation for parametrized partial differential equations and applications. J. Math. Ind. 1 (2011) 3. [CrossRef] [MathSciNet] [Google Scholar]
  23. S. Repin, A Posteriori Estimates for Partial Differential Equations, Walter de Gruyter, Berlin (2008). [Google Scholar]
  24. G. Rozza and K. Veroy, On the stability of the reduced basis method for Stokes equations in parametrized domains. Comput. Methods Appl. Mech. Eng. 196 (2007) 1244–1260. [Google Scholar]
  25. 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. Archives Comput. Methods Engrg. 15 (2008) 229–275. [Google Scholar]
  26. S. Sen, Reduced-basis approximation and a posteriori error estimation for many-parameter heat conduction problems. Numerical Heat Transfer, Part B: Fundamentals 54 (2008) 369–389. [Google Scholar]
  27. V.N. Temlyakov, Greedy Approximation. Acta Numerica (2008) 235–409. [Google Scholar]
  28. K. Veroy, Reduced-Basis Methods Applied to Problems in Elasticity: Analysis and Applications, MIT Thesis (2003). [Google Scholar]
  29. K. Veroy, C. Prudhomme, D.V. Rovas and A. Patera, A posteriori error bounds for reduced basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations, in Proc. 16th AIAA Comput. Fluid Dynamics Conf. (2003). Paper 2003–3847. [Google Scholar]
  30. S. Zhang, Efficient greedy algorithms for successive constraints methods with high-dimensional parameters, Brown Division of Applied Math Scientific Computing Tech Report 2011-23. [Google Scholar]

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