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All issues Volume 46 / No 4 (July-August 2012) ESAIM: M2AN, 46 4 (2012) 681-707 References
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Issue
ESAIM: M2AN
Volume 46, Number 4, July-August 2012
Page(s) 681 - 707
DOI https://doi.org/10.1051/m2an/2011047
Published online 03 February 2012
  1. U.M. Ascher, S.J. Ruuth and R.J. Spiteri, Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Special issue on time integration (Amsterdam, 1996). Appl. Numer. Math. 25 (1997) 151–167. [CrossRef] [MathSciNet] [Google Scholar]
  2. U.M. Ascher, S.J. Ruuth and B.T.R. Wetton, Implicit-explicit methods for time-dependent partial differential equations. SIAM J. Numer. Anal. 32 (1995) 797–823. [CrossRef] [Google Scholar]
  3. M. Braack, E. Burman, V. John and G. Lube, Stabilized finite element methods for the generalized Oseen problem. Comput. Methods Appl. Mech. Engrg. 196 (2007) 853–866. [CrossRef] [MathSciNet] [Google Scholar]
  4. A.N. Brooks and T.J.R. Hughes, Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. FENOMECH’81, Part I, Stuttgart (1981). Comput. Methods Appl. Mech. Engrg. 32 (1982) 199–259. [CrossRef] [MathSciNet] [Google Scholar]
  5. E. Burman, A unified analysis for conforming and nonconforming stabilized finite element methods using interior penalty. SIAM J. Numer. Anal. 43 (2005) 2012–2033 (electronic). [CrossRef] [Google Scholar]
  6. E. Burman, Consistent SUPG-method for transient transport problems : Stability and convergence. Comput. Methods Appl. Mech. Engrg. 199 (2010) 1114–1123. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. Burman and A. Ern, A continuous finite element method with face penalty to approximate Friedrichs’ systems. ESAIM : M2AN41 (2007) 55–76. [Google Scholar]
  8. E. Burman, A. Ern and M.A. Fernández, Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for first-order linear PDE systems. SIAM J. Numer. Anal. 48 (2010) 2019–2042. [CrossRef] [Google Scholar]
  9. E. Burman and M.A. Fernández, Finite element methods with symmetric stabilization for the transient convection-diffusion-reaction equation. Comput. Methods Appl. Mech. Engrg. 198 (2009) 2508–2519. [CrossRef] [MathSciNet] [Google Scholar]
  10. E. Burman and P. Hansbo, Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems. Comput. Methods Appl. Mech. Engrg. 193 (2004) 1437–1453. [CrossRef] [MathSciNet] [Google Scholar]
  11. E. Burman and G. Smith, Analysis of the space semi-discretized SUPG method for transient convection-diffusion equations. Technical report, University of Sussex (2010). [Google Scholar]
  12. E. Burman, J. Guzmán and D. Leykekhman, Weighted error estimates of the continuous interior penalty method for singularly perturbed problems. IMA J. Numer. Anal. 29 (2009) 284–314. [CrossRef] [Google Scholar]
  13. B. Cockburn and C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework. Math. Comp. 52 (1989) 411–435. [Google Scholar]
  14. R. Codina, Stabilized finite element approximation of transient incompressible flows using orthogonal subscales. Comput. Methods Appl. Mech. Engrg. 191 (2002) 4295–4321. [Google Scholar]
  15. M. Crouzeix, Une méthode multipas implicite-explicite pour l’approximation des équations d’évolution paraboliques. Numer. Math. 35 (1980) 257–276. [CrossRef] [Google Scholar]
  16. D.A. Di Pietro, A. Ern and J.-L. Guermond, Discontinuous Galerkin methods for anisotropic semidefinite diffusion with advection, SIAM J. Numer. Anal. 46 (2008) 805–831. [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements, Appl. Math. Sci. 159 (2004). [Google Scholar]
  18. A. Ern and J.-L. Guermond, Discontinuous Galerkin methods for Friedrichs’ systems. I. General theory. SIAM J. Numer. Anal. 44 (2006) 753–778. [CrossRef] [MathSciNet] [Google Scholar]
  19. J.-L. Guermond, Stabilization of Galerkin approximations of transport equations by subgrid modeling. ESAIM : M2AN 33 (1999) 1293–1316. [Google Scholar]
  20. J.-L. Guermond, Subgrid stabilization of Galerkin approximations of linear monotone operators. IMA J. Numer. Anal. 21 (2001) 165–197. [CrossRef] [MathSciNet] [Google Scholar]
  21. J. Guzmán, Local analysis of discontinuous Galerkin methods applied to singularly perturbed problems. J. Numer. Math. 14 (2006) 41–56. [CrossRef] [Google Scholar]
  22. F. Hecht, O. Pironneau, A. Le Hyaric and J. Morice, FreeFEM++, Version 3.14-0. http://www.freefem.org/ff++/. [Google Scholar]
  23. C. Johnson, U. Nävert and J. Pitkäranta, Finite element methods for linear hyperbolic problems. Comput. Methods Appl. Mech. Engrg. 45 (1984) 285–312. [CrossRef] [MathSciNet] [Google Scholar]
  24. C. Johnson and J. Pitkäranta, An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation. Math. Comp. 46 (1986) 1–26. [Google Scholar]
  25. P. Lesaint and P.-A. Raviart, On a finite element method for solving the neutron transport equation, in Mathematical aspects of Finite Elements in Partial Differential Equations, edited by C. de Boors. Academic Press (1974) 89–123. [Google Scholar]
  26. D. Levy and E. Tadmor, From semidiscrete to fully discrete : stability of Runge–Kutta schemes by the energy method. SIAM Rev. 40 (1998) 40–73 (electronic). [CrossRef] [Google Scholar]
  27. L. Pareschi and G. Russo, Implicit-explicit Runge–Kutta schemes and applications to hyperbolic systems with relaxation. J. Sci. Comput. 25 (2005) 129–155. [Google Scholar]
  28. H.-G. Roos, M. Stynes and L. Tobiska, Robust numerical methods for singularly perturbed differential equations, Convection-diffusion-reaction and flow problems. Springer Series in Computational Mathematics, 2nd edition. Springer-Verlag, Berlin 24 (2008). [Google Scholar]

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