Open Access
Volume 57, Number 1, January-February 2023
Page(s) 143 - 165
Published online 12 January 2023
  1. J.A. Evans and T.J. Hughes, Isogeometric divergence-conforming B-splines for the steady Navier–Stokes equations. Math. Models Methods Appl. Sci. 23 (2013) 1421–1478. [CrossRef] [MathSciNet] [Google Scholar]
  2. R.S. Falk and M. Neilan, Stokes complexes and the construction of stable finite elements with pointwise mass conservation. SIAM J. Numer. Anal. 51 (2013) 1308–1326. [CrossRef] [MathSciNet] [Google Scholar]
  3. J. Guzmán and M. Neilan, Conforming and divergence-free Stokes elements on general triangular meshes. Math. Comp. 83 (2014) 15–36. [Google Scholar]
  4. J. Guzmán and M. Neilan, Inf-sup stable finite elements on barycentric refinements producing divergence–free approximations in arbitrary dimensions. SIAM J. Numer. Anal. 56 (2018) 2826–2844. [CrossRef] [MathSciNet] [Google Scholar]
  5. 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]
  6. S. Zhang, A new family of stable mixed finite elements for the 3D Stokes equations. Math. Comp. 74 (2005) 543–554. [Google Scholar]
  7. D. Adalsteinsson and J.A. Sethian, A fast level set method for propagating interfaces. J. Comput. Phys. 118 (1995) 269–277. [CrossRef] [MathSciNet] [Google Scholar]
  8. D.M. Anderson, G.B. McFadden and A.A. Wheeler, Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30 (1998) 139–165. [CrossRef] [Google Scholar]
  9. M. Moës, J. Dolbow and T. Belytschko, A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46 (1999) 131–150. [CrossRef] [Google Scholar]
  10. E. Burman, S. Claus, P. Hansbo, M.G. Larson and A. Massing, CutFEM: discretizing geometry and partial differential equations. Int. J. Numer. Methods Eng. 104 (2015) 472–501. [CrossRef] [Google Scholar]
  11. L. Cattaneo, L. Formaggia, G.F. Iori, A. Scotti and P. Zunino, Stabilized extended finite elements for the approximation of saddle point problems with unfitted interfaces. Calcolo 52 (2015) 123–152. [CrossRef] [MathSciNet] [Google Scholar]
  12. E. Burman and P. Hansbo, Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes problem. ESAIM: M2AN 48 (2014) 859–874. [CrossRef] [EDP Sciences] [Google Scholar]
  13. J. Guzman and M. Olshanskii, Inf-sup stability of geometrically unfitted Stokes finite elements. Math. Comp. 87 (2018) 20891–2112. [Google Scholar]
  14. P. Hansbo, M.G. Larson and S. Zahedi, A cut finite element method for a Stokes interface problem. Appl. Numer. Math. 85 (2014) 90–114. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Kirchhart, S. Gross and A. Reusken, Analysis of an XFEM discretization for Stokes interface problems. SIAM J. Sci. Comput. 38 (2016) A1019–A1043. [CrossRef] [Google Scholar]
  16. G. Legrain, N. Moës and A. Huerta, Stability of incompressible formulations enriched with X-FEM. Comput. Methods Appl. Mech. Eng. 197 (2008) 1835–1849. [CrossRef] [Google Scholar]
  17. L. Scott and M. Vogelius, Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials. ESAIM: M2AN 19 (1985) 111–143. [CrossRef] [EDP Sciences] [Google Scholar]
  18. V. Girault and P.-A. Raviart, Finite element methods for Navier-Stokes equations: theory and algorithms, in Springer Series in Computational Mathematics 5, Springer-Verlag, Berlin (1986). [CrossRef] [Google Scholar]
  19. J. Guzmán and L.R. Scott, The Scott-Vogelius finite elements revisited. Math. Comp. 88 (2019) 515–529. [Google Scholar]
  20. S. Zhang, Divergence-free finite elements on tetrahedral grids for k ≥ 6. Math. Comp. 80 (2011) 669–695. [CrossRef] [MathSciNet] [Google Scholar]
  21. D.N. Arnold and J. Qin, Quadratic velocity/linear pressure Stokes elements, in Advances in Computer Methods for Partial Differential Equations–VII, Edited by R. Vichnevetsky, D. Knight, and G. Richter. IMACS (1992) 28–34. [Google Scholar]
  22. H. Liu, M. Neilan and B. Otus, A divergence-free finite element method for the Stokes problem with boundary correction. Preprint (2021). [Google Scholar]
  23. A. Hansbo and P. Hansbo, An unfitted finite element method, based on Nitsches method, for elliptic interface problems. Comput. Methods Appl. Mech. Eng. 191 (2002) 5537–5552. [CrossRef] [Google Scholar]
  24. M.A. Olshanskii, A low order Galerkin finite element method for the Navier–Stokes equations of steady incompressible flow: a stabilization issue and iterative methods. Comput. Methods Appl. Mech. Eng. 191 (2002) 5515–5536. [CrossRef] [Google Scholar]
  25. G. Fu, J. Guzman and M. Neilan, Exact smooth piecewise polynomial sequences on Alfeld splits. Math. Comp. 89 (2020) 1059–1091. [CrossRef] [MathSciNet] [Google Scholar]
  26. M.-J. Lai and L.L. Schumaker, Spline functions on triangulations, in Encyclopedia of Mathematics and its Applications, 110. Cambridge University Press, Cambridge (2007). [Google Scholar]
  27. C. Lehrenfeld, High order unfitted finite element methods on level set domains using isoparametric mappings. Comput. Methods Appl. Mech. Eng. 300 (2016) 716–733. [Google Scholar]
  28. A. Massing, M.G. Larson, A. Logg and M.E. Rognes, A stabilized Nitsche fictitious domain method for the Stokes problem. J. Sci. Comput. 61 (2018) 604–628. [Google Scholar]
  29. E. Burman and P. Hansbo, Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method. Appl. Numer. Math. 62 (2012) 328–341. [Google Scholar]
  30. E.M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, NJ (1970). [Google Scholar]
  31. M. Costabel and A. McIntosh, On Bogovski and regularized Poincaré integral operators for de Rham complexes on Lipschitz domains. Math. Z. 265 (2010) 297–320. [Google Scholar]
  32. C.M. Elliott and T. Ranner, Finite element analysis for a coupled bulk-surface partial differential equation. IMA J. Numer. Anal. 33 (2013) 377–402. [CrossRef] [MathSciNet] [Google Scholar]
  33. M. Fabien, J. Guzmán, M. Neilan and A. Zytoon, Low-order divergence-free approximations for the Stokes problem on Worsey-Farin and Powell-Sabin splits. Comput. Methods Appl. Mech. Eng. 390 (2022) 114444. [CrossRef] [Google Scholar]
  34. J. Guzmán, A. Lischke and M. Neilan, Exact sequences on Powell-Sabin splits. Calcolo 57 (2020) 13. [CrossRef] [Google Scholar]
  35. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483–493. [CrossRef] [MathSciNet] [Google Scholar]

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