Open Access
Issue
ESAIM: M2AN
Volume 57, Number 1, January-February 2023
Page(s) 1 - 27
DOI https://doi.org/10.1051/m2an/2022078
Published online 12 January 2023
  1. J.J. Duderstadt and L.J. Hamilton, Nuclear Reactor Analysis. John Wiley & Sons Inc., New York (1976). [Google Scholar]
  2. P. Ciarlet, Jr., E. Jamelot and F.D. Kpadonou, Domain decomposition methods for the diffusion equation with low-regularity solution. Comput. Math. App. 74 (2017) 2369–2384. [Google Scholar]
  3. P. Ciarlet, Jr., L. Giret, E. Jamelot and F.D. Kpadonou, Numerical analysis of the mixed finite element method for the neutron diffusion eigenproblem with heterogeneous coefficients. ESAIM: Math. Modell. Numer. Anal. 52 (2018) 2003–2035. [CrossRef] [EDP Sciences] [Google Scholar]
  4. C. Carstensen, A posteriori error estimate for the mixed finite element method. Math. Comp. 66 (1997) 465–476. [Google Scholar]
  5. M.G. Larson and A. Målqvist, A posteriori error estimates for mixed finite element approximations of elliptic problems. Numer. Math. 108 (2008) 487–500. [Google Scholar]
  6. C. Lovadina and R. Stenberg, Energy norm a posteriori error estimates for mixed finite element methods. Math. Comp. 75 (2006) 1659–1674. [Google Scholar]
  7. M. Vohralk, Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods. Math. Comp. 79 (2010) 2001–2032. [Google Scholar]
  8. B. Wohlmuth and R. Hoppe, A comparison of a posteriori error estimators for mixed finite element discretizations by Raviart-Thomas elements. Math. Comp. 68 (1999) 1347–1378. [Google Scholar]
  9. M.F. Wheeler and I. Yotov, A posteriori error estimates for the mortar mixed finite element method. SIAM J. Numer. Anal. 43 (2005) 1021–1042. [Google Scholar]
  10. M. Vohralk, A posteriori error estimates for lowest-order mixed finite element discretizations of convection-diffusion-reaction equations. SIAM J. Numer. Anal. 45 (2007) 1570–1599. [Google Scholar]
  11. E. Jamelot, A.-M. Baudron and J.-J. Lautard, Domain decomposition for the SPN solver MINOS. Transp. Theory Stat. Phys. 41 (2012) 495–512. [Google Scholar]
  12. E. Jamelot and P. Ciarlet, Jr., Fast non-overlapping Schwarz domain decomposition methods for solving the neutron diffusion equation. J. Comput. Phys. 241 (2013) 445–463. [CrossRef] [MathSciNet] [Google Scholar]
  13. A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements. Springer-Verlag, Berlin (2004). [Google Scholar]
  14. P.-A. Raviart and J.-M. Thomas, A mixed finite element method for second order elliptic problems. In Mathematical Aspects of Finite Element Methods. Vol. 606 of Lecture Notes in Mathematics. (1977) 292–315. [Google Scholar]
  15. J.-C. Nédélec, Mixed finite elements in ℝ3. Numer. Math. 35 (1980) 315–341. [Google Scholar]
  16. D. Boffi, F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods and Applications. Springer-Verlag, Berlin (2013). [Google Scholar]
  17. L. Giret, Non-conforming domain decomposition for the multigroup neutron SPN equations. Ph.D. thesis, Université Paris Saclay (2018). [Google Scholar]
  18. P. Oswald, On a BPX-preconditioner for P1 elements. Computing 51 (1993) 125–133. [CrossRef] [MathSciNet] [Google Scholar]
  19. T. Arbogast and Z. Chen, On the implementation of mixed methods as nonconforming methods for second-order elliptic problems. Math. Comp. 64 (1995) 943–972. [Google Scholar]
  20. F. Févotte, Une méthode de post-traitement des éléments finis de Raviart-Thomas appliquée à la neutronique. CMAP Seminar, Palaiseau, May 21 (2019). [Google Scholar]
  21. A. Ern and M. Vohralík, A posteriori error estimation based on potential and flux reconstruction for the heat equation. SIAM J. Numer. Anal. 48 (2010) 198–223. [Google Scholar]
  22. L.E. Payne and H.F. Weinberger, An optimal Poincaré inequality for convex domains. Arch. Ration. Mech. Anal. 5 (1960) 286–292. [Google Scholar]
  23. M. Bebendorf, A note on the Poincaré inequality for convex domains. Zeitschrift für Analysis und ihre Anwendungen 22 (2003) 751–756. [Google Scholar]
  24. W. Prager and J.L. Synge, Approximation in elasticity based on the concept of functions spaces. Q. Appl. Math. 5 (1947) 241–269. [Google Scholar]
  25. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. Vol. 40 of Classics in Applied Mathmetics. SIAM (2002). [Google Scholar]
  26. I. Cheddadi, R. Fučík, M.I. Prieto and M. Vohralk, Guaranteed and robust a posteriori error estimates for singularly perturbed reaction–diffusion problems. ESAIM: Math. Modell. Numer. Anal. 43 (2009) 867–888. [CrossRef] [EDP Sciences] [Google Scholar]
  27. R. Verfürth, Robust a posteriori error estimators for a singularly perturbed reaction–diffusion equation. Numer. Math. 78 (1998) 479–493. [Google Scholar]
  28. R. Verfürth, A posteriori error estimation and adaptive mesh-refinement techniques. J. Comput. Appl. Math. 50 (1994) 67–83. [Google Scholar]
  29. I. Babuška, B.A. Szabo and I.N. Katz, The p-version of the finite element method. SIAM J. Numer. Anal. 18 (1981) 515–545. [Google Scholar]
  30. W. Cao, W. Huang and R.D. Russell, An r-adaptive finite element method based upon moving mesh PDEs. J. Comput. Phys. 149 (1999) 221–244. [CrossRef] [MathSciNet] [Google Scholar]
  31. I. Babuška, M. Suri, The p and hp versions of the finite element method, basic principles and properties. SIAM Rev. 36 (1994) 578–632. [Google Scholar]
  32. P. Daniel, A. Ern, I. Smears and M. Vohralk, An adaptive hp-refinement strategy with computable guaranteed bound on the error reduction factor. Comput. Math. Applic. 76 (2018) 967–983. [CrossRef] [Google Scholar]
  33. J. Lang, W. Cao, W. Huang and R.D. Russell, A two-dimensional moving finite element method with local refinement based on a posteriori error estimates. Appl. Numer. Math. 46 (2003) 75–94. [CrossRef] [MathSciNet] [Google Scholar]
  34. W. Dörfler, A convergent adaptive algorithm for Poisson's equation. SIAM J. Numer. Anal. 33 (1996) 1106–1124. [Google Scholar]
  35. M. Dauge, Benchmark computations for Maxwell equations for the approximation of highly singular solutions. Available at: https://perso.univ-rennes1.fr/monique.dauge/core/index.html (2004). [Google Scholar]

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