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All issues Volume 59 / No 4 (July-August 2025) ESAIM: M2AN, 59 4 (2025) 1791-1829 References
Open Access
Issue
ESAIM: M2AN
Volume 59, Number 4, July-August 2025
Page(s) 1791 - 1829
DOI https://doi.org/10.1051/m2an/2025028
Published online 04 July 2025
  1. R.A. Adams, Sobolev Spaces. Academic Press, New York (1975). [Google Scholar]
  2. I. Babuška, Error bound for the finite element method. Num. Math. 16 (1971) 322–333. [CrossRef] [Google Scholar]
  3. I. Babuška, The finite element method with Lagrangian multipliers. Num. Math. 20 (1973) 179–192. [CrossRef] [Google Scholar]
  4. F. Bertrand and V. Ruas, A variant of the Raviart–Thomas method for smooth domains using straight-edged triangles. Preprint arXiv:2307.03503 (2025). [Google Scholar]
  5. F. Bertrand and G. Starke, Parametric Raviart–Thomas mixed methods on domains with curved surfaces. SIAM J. Numer. Anal. 54 (2016) 3648–3667. [CrossRef] [MathSciNet] [Google Scholar]
  6. F. Bertrand, S. Münzenmaier and G. Starke, First-order system least-squares on curved boundaries: higher-order Raviart–Thomas elements. SIAM J. Num. Anal. 52 (2014) 3165–3180. [CrossRef] [Google Scholar]
  7. E.K. Blum, Numerical Analysis and Computation: Theory and Practice. Addison Wesley (1972). [Google Scholar]
  8. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Texts Appl. Math. Vol. 15. Springer (2008). [CrossRef] [Google Scholar]
  9. F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. RAIRO Anal. Numér. 8 (1974) 129–151. [Google Scholar]
  10. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag (1991). [CrossRef] [Google Scholar]
  11. F. Brezzi, J. Douglas Jr. and D. Marini, Two families of mixed finite elements for second order elliptic problems. Numer. Math. 47 (1985) 217–235. [CrossRef] [MathSciNet] [Google Scholar]
  12. F. Brezzi, J. Douglas Jr., R. Durán and M. Fortin, Mixed finite elements for second order elliptic problems in three variables. Numer. Math. 51 (1987) 237–250. [CrossRef] [MathSciNet] [Google Scholar]
  13. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North Holland (1978). [Google Scholar]
  14. P.G. Ciarlet, Three-Dimensional Elasticity. Vol. 1. Elsevier Science (1994). [Google Scholar]
  15. P.G. Ciarlet and P.A. Raviart, The combined effect of curved boundaries and numerical integration in isoparametric finite element methods, in The Mathematical Foundations of the Finite Element Method with Applications to Part. Diff. Eqns., edited by A.K. Aziz. Academic Press (1972) 409–474. [Google Scholar]
  16. J.A. Cuminato and V. Ruas, Unification of distance inequalities for linear variational problems. Comput. Appl. Math. 34 (2015) 1009–1033. [CrossRef] [MathSciNet] [Google Scholar]
  17. E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136 (2012) 521–573. [Google Scholar]
  18. G. Duvaut and J.-L. Lions, Les Inéquations en Mécanique et en Physique. Dunod (1972). [Google Scholar]
  19. A. Ern and J.L. Guermond, Finite Elements I, Approximation and Interpolation. Springer (2021). [CrossRef] [Google Scholar]
  20. E.H. Georgoulis, Inverse-type estimates on hp-finite element spaces and applications. Math. Comput. 77 (2008) 201–219. [Google Scholar]
  21. V. Girault and P.A. Raviart, Finite Element Methods for Navier–Stokes Equations: Theory and Algorithms. Springer (1986). [Google Scholar]
  22. P. Grisvard, Elliptic Problems in Non Smooth Domains. Pitman Publ. Inc. (1985). [Google Scholar]
  23. A.J. Lew and M. Negri, Optimal convergence of a discontinuous-Galerkin-based immersed boundary method. ESAIM M2AN 45 (2011) 251–274. [Google Scholar]
  24. A. Quarteroni, R. Sacco and F. Saleri, Numerical Mathematics. Texts Appl. Math. Springer (2007). [Google Scholar]
  25. P.-A. Raviart and J.-M. Thomas, Mixed finite element methods for second order elliptic problems, in Lecture Notes in Mathematics. Vol. 606. Springer Verlag (1977) 292–315. [Google Scholar]
  26. V. Ruas, Optimal simplex finite-element approximations of arbitrary order in curved domains circumventing the isoparametric technique. Preprint arXiv:1701.00663 (2017). [Google Scholar]
  27. V. Ruas, Optimal Lagrange and Hermite finite elements for Dirichlet problems in curved domains with straight-edged triangles. ZAMM 100 (2020) e-2019002962020. [CrossRef] [Google Scholar]
  28. V. Ruas, Optimal-rate nonconforming finite-element solution of Dirichlet problems in curved domains with straight-edged tetrahedra. IMA J. Num. Anal. 41 (2021) 1368–1410. [CrossRef] [Google Scholar]
  29. V. Ruas, Success and failure of attempts to improve the accuracy of Raviart–Thomas mixed finite elements in curved domains. Examples Counterexamples 2 (2022) 100037. [CrossRef] [Google Scholar]
  30. V. Ruas, Fine error bounds for approximate asymmetric saddle point problems. Comput. Appl. Math. 43 (2024) 160. [CrossRef] [Google Scholar]
  31. V. Ruas and M.A. Silva Ramos, Efficiency on non parametric finite elements for optimal-order enforcement of Dirichlet conditions on curvilinear boundaries. J. Comput. Appl. Math. 394 (2021) 113523. [CrossRef] [Google Scholar]
  32. A.M. Sanchez and R. Arcangeli, Estimations des erreurs de meilleure approximation polynomiale et d’interpolation de Lagrange dans les espaces de Sobolev d’ordre non entier. Numer. Math. 45 (1984) 301–321. [CrossRef] [MathSciNet] [Google Scholar]
  33. D.B. Stein, R.D. Guy and B. Thomases, Immersed boundary smooth extension: a high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods. J. Comput. Phys. 304 (2016) 252–274. [CrossRef] [MathSciNet] [Google Scholar]
  34. G. Strang and G. Fix, An Analysis of the Finite Element Method. Prentice-Hall (1973). [Google Scholar]
  35. J.L. Taylor, S. Kim and R.M. Brown, The Green function for elliptic systems in two dimensions. Comm. Part. Differ. Eqns. 38 (2013) 1574–1600. [CrossRef] [Google Scholar]
  36. R. Verfürth, A Posteriori Error Estimation Techniques for Finite Element Methods. Oxford Sci. Publ. (2013). [CrossRef] [Google Scholar]
  37. O.C. Zienkiewicz, The Finite Element Method in Engineering Science. McGraw-Hill (1971). [Google Scholar]

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