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All issues Volume 55 / No 5 (September-October 2021) ESAIM: M2AN, 55 5 (2021) 2349-2364 References
Open Access
Issue
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
Page(s) 2349 - 2364
DOI https://doi.org/10.1051/m2an/2021059
Published online 21 October 2021
  1. G. Barrenechea, E. Burman and J. Guzmán, Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow. Math. Models Methods Appl. Sci. 30 (2020) 847–865. [CrossRef] [MathSciNet] [Google Scholar]
  2. D. Boffi, F. Brezzi and M. Fortin, Mixed finite element methods and applications. Heidelberg, Springer (2013). [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. Eng. 196 (2007) 853–866. [CrossRef] [Google Scholar]
  4. S. Brenner and R. Scott, The mathematical theory of finite element methods. Springer Science & Business Media (2007). [Google Scholar]
  5. E. Burman, M.A. Fernández and P. Hansbo, Continuous interior penalty finite element method for Oseen’s equations. SIAM J. Numer. Anal. 44 (2006) 1248–1274. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Cesmelioglu, B. Cockburn and W. Qiu, Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations. Math. Comput. 86 (2017) 1643–1670. [Google Scholar]
  7. R. Codina, Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales. Appl. Numer. Math. 58 (2008) 264–283. [Google Scholar]
  8. H. Dallmann, D. Arndt and G. Lube, Local projection stabilization for the Oseen problem. IMA J. Numer. Anal. 36 (2016) 796–823. [CrossRef] [MathSciNet] [Google Scholar]
  9. A. Ern and J.L. Guermond, Theory and Practice of Finite Elements. Appl. Math. Sci. 159, Springer-Verlag, New York (2004). [CrossRef] [Google Scholar]
  10. N. Fehn, M. Kronbichler, C. Lehrenfeld, G. Lube and P.W. Schroeder, High-order DG solvers for underresolved turbulent incompressible flows: A comparison of L2 and H(div) methods. Int. J. Numer. Methods Fluids 91 (2019) 533–556. [CrossRef] [Google Scholar]
  11. G. Fu, An explicit divergence-free DG method for incompressible flow. Comput. Methods Appl. Mech. Eng. 345 (2019) 502–517. [CrossRef] [Google Scholar]
  12. B. García-Archilla, V. John and J. Novo, Symmetric pressure stabilization for equal-order finite element approximations to the time-dependent Navier-Stokes equations. IMA J. Numer. Anal. 41 (2021) 1093–1129. [CrossRef] [MathSciNet] [Google Scholar]
  13. G.N. Gatica, A simple introduction to the mixed finite element method. Theory and Applications. Springer Briefs in Mathematics, Springer, London (2014). [Google Scholar]
  14. J. Guzmán, C.W. Shu and F.A. Sequeira, H(div) conforming and DG methods for incompressible Euler’s equations. IMA J. Numer. Anal. 37 (2017) 1733–1771. [MathSciNet] [Google Scholar]
  15. Y. Han and Y. Hou, Robust error analysis of H(div)-conforming DG method for the time-dependent incompressible Navier-Stokes equations. J. Comput. Appl. Math. 390 (2021) 113365. [CrossRef] [Google Scholar]
  16. T.L. Horváth and S. Rhebergen, A locally conservative and energy-stable finite-element method for the Navier-Stokes problem on time-dependent domains. Int. J. Numer. Methods Fluids 89 (2019) 519–532. [CrossRef] [Google Scholar]
  17. T.L. Horváth and S. Rhebergen, An exactly mass conserving space-time embedded-hybridized discontinuous Galerkin method for the Navier-Stokes equations on moving domains. J. Comput. Phys. 417 (2020) 109577. [CrossRef] [MathSciNet] [Google Scholar]
  18. K.L.A. Kirk and S. Rhebergen, Analysis of a pressure-robust hybridized discontinuous Galerkin method for the stationary Navier-Stokes equations. J. Sci. Comput. 81 (2019) 881–897. [CrossRef] [MathSciNet] [Google Scholar]
  19. R.J. Labeur and G.N. Wells, Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations. SIAM J. Sci. Comput. 34 (2012) A889–A913. [CrossRef] [Google Scholar]
  20. P.L. Lederer and S. Rhebergen, A pressure-robust embedded discontinuous Galerkin method for the Stokes problem by reconstruction operators. SIAM J. Numer. Anal. 8 (2020) 2915–2933. [CrossRef] [MathSciNet] [Google Scholar]
  21. P.L. Lederer, C. Lehrenfeld and J. Schöberl, Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. Part II.. ESAIM: M2AN 53 (2019) 503–522. [CrossRef] [EDP Sciences] [Google Scholar]
  22. C. Lehrenfeld and J. Schöberl, High order exactly divergence-free hybrid discontinuous Galerkin methods for unsteady incompressible flows. Comput. Methods Appl. Mech. Eng. 307 (2016) 339–361. [CrossRef] [Google Scholar]
  23. A. Natale and C.J. Cotter, A variational finite-element discretization approach for perfect incompressible fluids. IMA J. Numer. Anal. 38 (2018) 1388–1419. [CrossRef] [MathSciNet] [Google Scholar]
  24. D.D.A. Pietro and J. Droniou, The Hybrid High-Order Method for Polytopal Meshes: Design, Analysis, and Applications. Springer (2020). [CrossRef] [Google Scholar]
  25. S. Rhebergen and G. Wells, Analysis of a hybridized/interface stabilized finite element method for the Stokes equations. SIAM J. Numer. Anal. 55 (2017) 1982–2003. [CrossRef] [MathSciNet] [Google Scholar]
  26. S. Rhebergen and G.N. Wells, A hybridizable discontinuous Galerkin method for the Navier-Stokes equations with pointwise divergence-free velocity field. J. Sci. Comput. 76 (2018) 1484–1501. [CrossRef] [MathSciNet] [Google Scholar]
  27. S. Rhebergen and G.N. Wells, Preconditioning of a hybridized discontinuous Galerkin finite element method for the Stokes equations. J. Sci. Comput. 77 (2018) 1936–1952. [CrossRef] [MathSciNet] [Google Scholar]
  28. S. Rhebergen and G.N. Wells, An embedded-hybridized discontinuous Galerkin finite element method for the Stokes equations. Comput. Methods Appl. Mech. Eng. 358 (2020) 112619. [CrossRef] [Google Scholar]
  29. J. Schöberl, C++ 11 implementation of finite elements in NGSolve. Institute for analysis and scientific computing, Vienna University of Technology (2014). [Google Scholar]
  30. P.W. Schroeder and G. Lube, Divergence-free H(div)-FEM for time-dependent incompressible flows with applications to high Reynolds number vortex dynamics. J. Sci. Comput. 75 (2018) 830–858. [CrossRef] [MathSciNet] [Google Scholar]

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