Error control for the localized reduced basis multi-scale method with adaptive on-line enrichment

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Ohlberger, Mario; Schindler, Felix;
(2015)
  • Related identifiers: doi: 10.1137/151003660
  • Subject: G.1.8 | 65G99, 65N55, 65N15, 35J20, 65N30, 76S05 | Mathematics - Numerical Analysis

In this contribution we consider localized, robust and efficient a-posteriori error estimation of the localized reduced basis multi-scale (LRBMS) method for parametric elliptic problems with possibly heterogeneous diffusion coefficient. The numerical treatment of such p... View more
  • References (13)
    13 references, page 1 of 2

    [1] dune-pdelab. Version: February 2014

    [2] Abdulle, A.: Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales. In: Math. Comp. 81 (2012), Nr. 278, 687-713. http://dx.doi.org/10.1090/S0025-5718-2011-02527-5. - DOI 10.1090/S0025-5718-2011-02527-5. - ISSN 0025-5718 Nr. 2021, 20130388. http://dx.doi.org/10.1098/Rrsta.2013.0388. - DOI

    [4] Abdulle, A. ; Bai, Y.: Reduced-order modelling numerical homogenization. In: Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 372 (2014), 10.1098/rsta.2013.0388. - ISSN 1364-503X

    [11] Bastian, P. ; Blatt, M. ; Dedner, A. ; Engwer, C. ; Klöfkorn, R. ; Kornhuber, R. ; Ohlberger, M. ; Sander, O.: A generic grid interface for parallel and adaptive scientific computing. II. Implementation and tests in DUNE. In: Computing 82 (2008), Nr. 2-3, 121-138. http://dx.doi.org/10.1007/s00607-008-0004-9. - DOI 10.1007/s00607-008-0004-9. - ISSN 0010-485X

    [12] Bastian, P. ; Blatt, M. ; Dedner, A. ; Engwer, C. ; Klöfkorn, R. ; Ohlberger, M. ; Sander, O.: A generic grid interface for parallel and adaptive scientific computing. I. Abstract framework. In: Computing 82 (2008), Nr. 2-3, 103- 119. http://dx.doi.org/10.1007/s00607-008-0003-x. - DOI 10.1007/s00607- 008-0003-x. - ISSN 0010-485X

    [32] Henning, P. ; Peterseim, D.: Oversampling for the multiscale finite element method. In: Multiscale Model. Simul. 11 (2013), Nr. 4, 1149-1175. http://dx.doi. org/10.1137/120900332. - DOI 10.1137/120900332. - ISSN 1540-3459

    [42] Morin, P. ; Nochetto, R. H. ; Siebert, K. G.: Convergence of adaptive finite element methods. In: SIAM Rev. 44 (2002), Nr. 4, 631-658 (2003). http: //dx.doi.org/10.1137/S0036144502409093. - DOI 10.1137/S0036144502409093. - ISSN 0036-1445. - Revised reprint of “Data oscillation and convergence of adaptive FEM” [SIAM J. Numer. Anal. 38 (2000), no. 2, 466-488 (electronic); MR1770058 (2001g:65157)]

    [43] Nordbotten, J. M.: Adaptive variational multiscale methods for multiphase flow in porous media. In: Multiscale Model. Simul. 7 (2008), Nr. 3, 1455-1473. http: //dx.doi.org/10.1137/080724745. - DOI 10.1137/080724745. - ISSN 1540-3459

    [44] Ohlberger, M.: Error control based model reduction for multiscale problems. In: Proceedings of Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012, Slovak University of Technology in Bratislava, Publishing House of STU, 2012. - ISSN 978-80-227-3742-5, S. 1-10

    [53] Society of Petroleum Engineers: 2001 SPE Comparative Solution Project. http://www.spe.org/web/csp/index.html. Version: 2001

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