Open Access
Issue
ESAIM: M2AN
Volume 56, Number 1, January-February 2022
Page(s) 349 - 383
DOI https://doi.org/10.1051/m2an/2021084
Published online 14 February 2022
  1. G. Akrivis, Implicit-explicit multistep methods for nonlinear parabolic equations. Math. Comp. 82 (2013) 45–68. [Google Scholar]
  2. G. Akrivis, Stability of implicit and implicit-explicit multistep methods for nonlinear parabolic equations. IMA J. Numer. Anal. 38 (2018) 1768–1796. [CrossRef] [MathSciNet] [Google Scholar]
  3. G. Akrivis, M. Crouzeix and C. Makridakis, Implicit-explicit multistep finite element methods for nonlinear parabolic problems. Math. Comp. 67 (1998) 457–477. [CrossRef] [MathSciNet] [Google Scholar]
  4. 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] [MathSciNet] [Google Scholar]
  5. U.M. Ascher, S.J. Ruuth and R.J. Spiteri, Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Appl. Numer. Math. 25 (1997) 151–167. Special issue on time integration (Amsterdam, 1996). [Google Scholar]
  6. G.A. Baker, V.A. Dougalis and O.A. Karakashian, On a higher order accurate fully discrete Galerkin approximation to the Navier-Stokes equations. Math. Comp. 39 (1982) 339–375. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. Burman and A. Ern, Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations. Math. Comp. 76 (2007) 1119–1140. [CrossRef] [MathSciNet] [Google Scholar]
  8. E. Burman and A. Ern, Implicit-explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations. ESAIM: M2AN 46 (2012) 681–707. [CrossRef] [EDP Sciences] [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. Eng. 198 (2009) 2508.2519. [CrossRef] [Google Scholar]
  10. 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] [MathSciNet] [Google Scholar]
  11. E. Burman, A. Ern and M.A. Fernández, Fractional-step methods and finite elements with symmetric stabilization for the transient Oseen problem. ESAIM: M2AN 51 (2017) 487–507. [CrossRef] [EDP Sciences] [Google Scholar]
  12. 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]
  13. M. Crouzeix, Une méthode multipas implicite-explicite pour l’approximation des équations d’évolution paraboliques. Numer. Math. 35 (1980) 257–276. [Google Scholar]
  14. C. Dawson, Godunov-mixed methods for advection-diffusion equations in multidimensions. SIAM J. Numer. Anal. 30 (1993) 1315–1332. [CrossRef] [MathSciNet] [Google Scholar]
  15. J. Douglas Jr and T. Dupont, Galerkin methods for parabolic equations. SIAM J. Numer. Anal. 7 (1970) 575–626. [CrossRef] [MathSciNet] [Google Scholar]
  16. M.L. Ghrist, B. Fornberg and J.A. Reeger, Stability ordinates of Adams predictor-corrector methods. BIT 55 (2015) 733–750. [CrossRef] [MathSciNet] [Google Scholar]
  17. W. Hundsdorfer, Trapezoidal and midpoint splittings for initial-boundary value problems. Math. Comp. 67 (1998) 1047–1062. [CrossRef] [MathSciNet] [Google Scholar]
  18. W. Hundsdorfer, Partially implicit BDF2 blends for convection dominated flows. SIAM J. Numer. Anal. 38 (2001) 1763–1783. [CrossRef] [MathSciNet] [Google Scholar]
  19. 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. [CrossRef] [MathSciNet] [Google Scholar]
  20. A. Mazzia, L. Bergamaschi, C.N. Dawson and M. Putti, Godunov mixed methods on triangular grids for advection-dispersion equations. Comput. Geosci. 6 (2002) 123–139. [CrossRef] [MathSciNet] [Google Scholar]
  21. R.C. Moura, A. Cassinelli, A.F.C. da Silva, E. Burman and S.J. Sherwin, Gradient jump penalty stabilisation of spectral/hp element discretisation for under-resolved turbulence simulations. Comput. Methods Appl. Mech. Eng. 388 (2022) 114200. [CrossRef] [Google Scholar]
  22. A.K. Pani, V. Thomée and A.S. Vasudeva Murthy, A first-order explicit-implicit splitting method for a convection-diffusion problem. Comput. Methods Appl. Math. 20 (2020) 769–782. [CrossRef] [MathSciNet] [Google Scholar]
  23. V. Thomée, Galerkin Finite Element Methods for Parabolic Problems. Vol. 25 of Springer Series in Computational Mathematics, 2nd edition. Springer-Verlag, Berlin (2006). [Google Scholar]
  24. J.M. Varah, Stability restrictions on second order, three level finite difference schemes for parabolic equations. SIAM J. Numer. Anal. 17 (1980) 300–309. [CrossRef] [MathSciNet] [Google Scholar]
  25. H. Wang, Y. Liu, Q. Zhang and C.-W. Shu, Local discontinuous Galerkin methods with implicit-explicit time-marching for time-dependent incompressible fluid flow. Math. Comp. 88 (2019) 91–121. [Google Scholar]
  26. H. Wang, Q. Zhang and C.-W. Shu, Implicit-explicit local discontinuous Galerkin methods with generalized alternating numerical fluxes for convection-diffusion problems. J. Sci. Comput. 81 (2019) 2080–2114. [CrossRef] [MathSciNet] [Google Scholar]
  27. Q. Zhang and C.-W. Shu, Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws. SIAM J. Numer. Anal. 42 (2004) 641–666. [Google Scholar]
  28. Q. Zhang and C.-W. Shu, Stability analysis and a priori error estimates of the third order explicit Runge-Kutta discontinuous Galerkin method for scalar conservation laws. SIAM J. Numer. Anal. 48 (2010) 1038–1063. [Google Scholar]

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