EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 59 / No 2 (March-April 2025) ESAIM: M2AN, 59 2 (2025) 1075-1094 References
Open Access
Issue
ESAIM: M2AN
Volume 59, Number 2, March-April 2025
Page(s) 1075 - 1094
DOI https://doi.org/10.1051/m2an/2025015
Published online 02 April 2025
  1. V.I. Arnold and B.A. Khesin, Topological Methods in Hydrodynamics. Vol. 19. Springer (2009). [Google Scholar]
  2. L. Beirão da Veiga, F. Dassi, G. Manzini and L. Mascotto, The virtual element method for the 3D resistive magne-tohydrodynamic model. Math. Models Methods Appl. Sci. 33 (2023) 643–686. [CrossRef] [MathSciNet] [Google Scholar]
  3. L. Beirão da Veiga, F. Dassi and G. Vacca, Pressure and convection robust finite elements for magnetohydrodynamics. Preprint arXiv:2405.05434 (2024). [Google Scholar]
  4. L. Beirão da Veiga, F. Dassi and G. Vacca, Robust finite elements for linearized magnetohydrodynamics. SIAM J. Numer. Anal. 62 (2024) 1539–1564. [Google Scholar]
  5. D. Boffi and L. Gastaldi, Interpolation estimates for edge finite elements and application to band gap computation. Appl. Numer. Math. 56 (2006) 1283–1292. [MathSciNet] [Google Scholar]
  6. D. Boffi, F. Brezzi and M. Fortin, Mixed Finite Element Methods and Applications. Vol. 44. Springer (2013). [Google Scholar]
  7. A. Buffa and P. Ciarlet, On traces for functional spaces related to Maxwell’s equations Part II: Hodge decompositions on the boundary of Lipschitz polyhedra and applications. Math. Methods Appl. Sci. 24 (2001) 31–48. [CrossRef] [MathSciNet] [Google Scholar]
  8. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. SIAM (2002). [Google Scholar]
  9. P. Constantin, E. Weinan and E.S. Titi, Onsager’s conjecture on the energy conservation for solutions of Euler’s equation. Comm. Math. Phys. 165 (1994) 207–209. [MathSciNet] [Google Scholar]
  10. J. Douglas, T. Dupont and L. Wahlbin, The stability in Lq of the L2 projection into finite element function spaces. Numer. Math. 23 (1974) 193–197. [Google Scholar]
  11. A. Ern and J.-L. Guermond, Finite element quasi-interpolation and best approximation. ESAIM Math. Model. Numer. Anal. 51 (2017) 1367–1385. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  12. A. Ern and J.-L. Guermond, Finite Elements I: Approximation and Interpolation. Vol. 72. Springer Nature (2021). [Google Scholar]
  13. N. Fehn, M. Kronbichler, P. Munch and W.A. Wall, Numerical evidence of anomalous energy dissipation in incompressible Ruler flows: towards grid-converged results for the inviscid Taylor–Green problem. J. Fluid Mech. 932 (2022) A40. [Google Scholar]
  14. H. Gao, W. Qiu and W. Sun, New analysis of mixed FEMs for dynamical incompressible magnetohydrodynamics. Numer. Math. 153 (2023) 327–358. [Google Scholar]
  15. E.S. Gawlik and F. Gay-Balmaz, A finite element method for MHD that preserves energy, cross-helicity, magnetic helicity, incompressibility, and div B = 0. J. Comput. Phys. 450 (2022) 110847. [Google Scholar]
  16. J.-F. Gerbeau, C. Le Bris and T. Lelièvre, Mathematical Methods for the Magnetohydrodynamics of Liquid Metals. Clarendon Press (2006). [Google Scholar]
  17. M.D. Gunzburger, A.J. Meir and J.S. Peterson, On the existence, uniqueness, and finite element approximation of solutions of the equations of stationary, incompressible magnetohydrodynamics. Math. Comp. 56 (1991) 523–563. [CrossRef] [MathSciNet] [Google Scholar]
  18. M. He, K. Hu and P.E. Farrell, Topological-preserving computation for magnetic relaxation. In preparation (2024). [Google Scholar]
  19. R. Hiptmair, L. Li, S. Mao and W. Zheng, A fully divergence-free finite element method for magnetohydrodynamic equations. Math. Models Methods Appl. Sci. 28 (2018) 659–695. [CrossRef] [MathSciNet] [Google Scholar]
  20. K. Hu and J. Xu, Structure-preserving finite element methods for stationary MHD models. Math. Comp. 88 (2019) 553–581. [Google Scholar]
  21. K. Hu, Y. Ma and J. Xu, Stable finite element methods preserving ∇ · B = 0 exactly for MHD models. Numer. Math. 135 (2017) 371–396. [CrossRef] [MathSciNet] [Google Scholar]
  22. K. Hu, W. Qiu and K. Shi, Convergence of a BE based finite element method for MHD models on Lipschitz domains. J. Comput. Appl. Math. 368 (2020) 112477. [Google Scholar]
  23. K. Hu, Y.-J. Lee and J. Xu, Helicity-conservative finite element discretization for incompressible MHD systems. J. Comput. Phys. 436 (2021) 110284. [Google Scholar]
  24. P. Isett, A proof of Onsager’s conjecture. Ann. Math. 188 (2018) 871–963. [CrossRef] [MathSciNet] [Google Scholar]
  25. F. Laakmann, K. Hu and P.E. Farrell, Structure-preserving and helicity-conserving finite element approximations and preconditioning for the Hall MHD equations. J. Comput. Phys. 492 (2023) 112410. [Google Scholar]
  26. H. Lamb, Hydrodynamics. University Press (1924). [Google Scholar]
  27. W. Layton, Introduction to the Numerical Analysis of Incompressible Viscous Flows. SIAM (2008). [Google Scholar]
  28. H.K. Moffatt, The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35 (1969) 117–129. [NASA ADS] [CrossRef] [Google Scholar]
  29. H.K. Moffatt, Some developments in the theory of turbulence. J. Fluid Mech. 106 (1981) 27–47. [Google Scholar]
  30. P. Monk, Finite Element Methods for Maxwell’s Equations. Oxford University Press (2003). [Google Scholar]
  31. L. Onsager, Statistical hydrodynamics. Nuovo Cimento Soc. Ital. Fis. B 6 (1949) 279–287. [Google Scholar]
  32. D.I. Pontin and G. Hornig, The Parker problem: existence of smooth force-free fields and coronal heating. Living Rev. Sol. Phys. 17 (2020) 5. [CrossRef] [Google Scholar]
  33. L.G. Rebholz, An energy-and helicity-conserving finite element scheme for the Navier–Stokes equations. SIAM J. Numer. Anal. 45 (2007) 1622–1638. [CrossRef] [MathSciNet] [Google Scholar]
  34. D. Schötzau, Mixed finite element methods for stationary incompressible magneto-hydrodynamics. Numer. Math. 96 (2004) 771–800. [CrossRef] [MathSciNet] [Google Scholar]
  35. R. Shvydkoy, Lectures on the Onsager conjecture. Discrete Contin. Dyn. Syst. Ser. S 3 (2010) 473–496. [Google Scholar]
  36. Y. Zhang, A. Palha, M. Gerritsma and L.G. Rebholz, A mass-, kinetic energy-and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier–Stokes equations, part I: periodic domains. J. Comput. Phys. 451 (2022) 110868. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you