Free Access
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Page(s) S447 - S474
Published online 26 February 2021
  1. O. Axelsson, J. Karátson and B. Kovács, Robust preconditioning estimates for convection-dominated elliptic problems via a streamline Poincaré-Friedrichs inequality. SIAM J. Numer. Anal. 52 (2014) 2957–2976. [Google Scholar]
  2. B. Ayuso and L.D. Marini, Discontinuous Galerkin methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 47 (2009) 1391–1420. [Google Scholar]
  3. P. Azérad and J. Pousin, Inégalité de Poincaré courbe pour le traitement variationnel de l’équation de transport. C. R. Acad. Sci. Paris Sér. I Math. 322 (1996) 721–727. [Google Scholar]
  4. R. Becker, D. Capatina and R. Luce, Reconstruction-based a posteriori error estimators for the transport equation. In: Numerical Mathematics and Advanced Applications 2011. Springer, Berlin-Heidelberg (2013) 13–21. [Google Scholar]
  5. K.S. Bey and J.T. Oden, hp-version discontinuous Galerkin methods for hyperbolic conservation laws. Comput. Methods Appl. Mech. Eng. 133 (1996) 259–286. [Google Scholar]
  6. J. Blechta, J. Málek and M. Vohralk, Localization of the W−1,q norm for local a posteriori efficiency. IMA J. Numer. Anal. 40 (2019) 914–950. [Google Scholar]
  7. D. Braess, V. Pillwein and J. Schöberl, Equilibrated residual error estimates are p-robust. Comput. Methods Appl. Mech. Eng. 198 (2009) 1189–1197. [Google Scholar]
  8. P. Cantin, Well-posedness of the scalar and the vector advection-reaction problems in Banach graph spaces. C. R. Math. Acad. Sci. Paris 355 (2017) 892–902. [Google Scholar]
  9. P. Cantin and A. Ern, An edge-based scheme on polyhedral meshes for vector advection-reaction equations. ESAIM: M2AN 51 (2017) 1561–1581. [EDP Sciences] [Google Scholar]
  10. C. Carstensen and S.A. Funken, Fully reliable localized error control in the FEM. SIAM J. Sci. Comput. 21 (1999) 1465–1484. [Google Scholar]
  11. W. Dahmen and R.P. Stevenson, Adaptive strategies for transport equations. Comput. Methods Appl. Math. 19 (2019) 431–464. [Google Scholar]
  12. W. Dahmen, C. Huang, C. Schwab and G. Welper, Adaptive Petrov-Galerkin methods for first order transport equations. SIAM J. Numer. Anal. 50 (2012) 2420–2445. [Google Scholar]
  13. A. Devinatz, R. Ellis and A. Friedman, The asymptotic behavior of the first real eigenvalue of second order elliptic operators with a small parameter in the highest derivatives. II. Indiana Univ. Math. J. 23 (1973–1974) 991–1011. [CrossRef] [MathSciNet] [Google Scholar]
  14. A. Ern and J.-L. Guermond, Discontinuous Galerkin methods for Friedrichs’ systems. I. General theory. SIAM J. Numer. Anal. 44 (2006) 753–778. [Google Scholar]
  15. A. Ern and M. Vohralík, Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations. SIAM J. Numer. Anal. 53 (2015) 1058–1081. [Google Scholar]
  16. A. Ern and M. Vohralk, Stable broken H1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions. Math. Comput. 89 (2020) 551–594. [Google Scholar]
  17. A. Ern, A.F. Stephansen and M. Vohralík, Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems. J. Comput. Appl. Math. 234 (2010) 114–130. [Google Scholar]
  18. K.O. Friedrichs, Symmetric positive linear differential equations. Comm. Pure Appl. Math. 11 (1958) 333–418. [CrossRef] [MathSciNet] [Google Scholar]
  19. E.H. Georgoulis, E. Hall and C. Makridakis, Error control for discontinuous Galerkin methods for first order hyperbolic problems. In: Vol. 157 of Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations. IMA Vol. Math. Appl. Springer, Cham (2014) 195–207. [Google Scholar]
  20. E.H. Georgoulis, E. Hall and C. Makridakis, An a posteriori error bound for discontinuous Galerkin approximations of convection-diffusion problems. IMA J. Numer. Anal. 39 (2019) 34–60. [Google Scholar]
  21. J.-L. Guermond, A finite element technique for solving first-order PDEs in lp. SIAM J. Numer. Anal. 42 (2004) 714–737. [Google Scholar]
  22. F. Hecht, New development in FreeFEM++. J. Numer. Math. 20 (2012) 251–265. [CrossRef] [MathSciNet] [Google Scholar]
  23. P. Houston, J.A. Mackenzie, E. Süli and G. Warnecke, A posteriori error analysis for numerical approximations of Friedrichs systems. Numer. Math. 82 (1999) 433–470. [Google Scholar]
  24. P.D. Lax and R.S. Phillips, Local boundary conditions for dissipative symmetric linear differential operators. Comm. Pure Appl. Math. 13 (1960) 427–455. [CrossRef] [MathSciNet] [Google Scholar]
  25. C. Makridakis and R.H. Nochetto, A posteriori error analysis for higher order dissipative methods for evolution problems. Numer. Math. 104 (2006) 489–514. [Google Scholar]
  26. I. Muga, M.J. Tyler and K. van der Zee, The discrete-dual minimal-residual method (DDMRes) for weak advection-reaction problems in Banach spaces. Preprint arXiv:1808.04542 (2018). [Google Scholar]
  27. G. Sangalli, Analysis of the advection-diffusion operator using fractional order norms. Numer. Math. 97 (2004) 779–796. [Google Scholar]
  28. G. Sangalli, A uniform analysis of nonsymmetric and coercive linear operators. SIAM J. Math. Anal. 36 (2005) 2033–2048. [CrossRef] [MathSciNet] [Google Scholar]
  29. G. Sangalli, Robust a posteriori estimator for advection-diffusion-reaction problems. Math. Comput. 77 (2008) 41–70. [Google Scholar]
  30. D. Schötzau and L. Zhu, A robust a posteriori error estimator for discontinuous Galerkin methods for convection-diffusion equations. Appl. Numer. Math. 59 (2009) 2236–2255. [Google Scholar]
  31. E. Süli, A posteriori error analysis and adaptivity for finite element approximations of hyperbolic problems. In: An Introduction to Recent Developments in Theory and Numerics for Conservation Laws (Freiburg/Littenweiler, 1997) Vol. 5 of Lect. Notes Comput. Sci. Eng. Springer, Berlin-Heidelberg (1999) 123–194. [Google Scholar]
  32. Z. Tang, (2015). [Google Scholar]
  33. D.S. Tartakoff, Regularity of solutions to boundary value problems for first order systems. Indiana Univ. Math. J. 21 (1972) 1113–1129. [Google Scholar]
  34. R. Verfürth, Robust a posteriori error estimates for stationary convection–diffusion equations. SIAM J. Numer. Anal. 43 (2005) 1766–1782. [Google Scholar]
  35. M. Vohralk and M. Zakerzadeh, Guaranteed and robust L2-norm a posteriori error estimates for 1D linear advection–reaction problems. In preparation (2020). [Google Scholar]

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