Free Access
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Page(s) S301 - S321
Published online 26 February 2021
  1. R.A. Adams and J.J.F. Fournier, Sobolev Spaces, 2nd edition. In: Vol. 140 of Pure and Applied Mathematics. Elsevier (2003). [Google Scholar]
  2. J. Bergh and J. Löfström, Interpolation Spaces. An Introduction. In: Vol. 223 of Grundlehren der mathematischen Wissenschaften. Springer (1976). [CrossRef] [Google Scholar]
  3. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, 3rd edition. In: Vol. 15 of Texts in Applied Mathematics. Springer (2008). [CrossRef] [Google Scholar]
  4. E. Burman, La pénalisation fantôme. C.R. Math. 348 (2010) 1217–1220. [Google Scholar]
  5. J.-P. Chehab, A. Cohen, D. Jennequin, J. Nieto, C. Roland and J. Roche, An adaptive Particle-In-Cell method using multi-resolution analysis, edited by S. Cordier, T. Goudon, M. Gutnic and E. Sonnendrücker. In: Vol. 7 of Numerical Methods for Hyperbolic and Kinetic Problems. IRMA Lectures in Mathematics and Theoretical Physics. European Mathematical Society (2005) 29–42. [Google Scholar]
  6. A. Cohen and B. Perthame, Optimal approximations of transport equations by particle and pseudoparticle methods. SIAM J. Math. Anal. 32 (2000) 616–636. [CrossRef] [MathSciNet] [Google Scholar]
  7. G.-H. Cottet, A new approach for the analysis of vortex methods in two and three dimensions. Ann. Inst. Henri Poincaré. Anal. nonlin. 5 (1988) 227–285. [Google Scholar]
  8. G.-H. Cottet and P.D. Koumoutsakos, Vortex Methods. Cambridge University Press (2000). [Google Scholar]
  9. M. Crouzeix and V. Thomée, The stability in Lp and Formula of the L2-projection onto finite element function spaces. Math. Comput. 48 (1987) 521–532. [Google Scholar]
  10. W. Dahmen, R.A. De Vore and K. Scherer, Multi-dimensional spline approximation. SIAM J. Numer. Anal. 17 (1980) 380–402. [Google Scholar]
  11. P.J. Davis, A construction of nonnegative approximate quadratures. Math. Comput. 21 (1967) 578–582. [Google Scholar]
  12. R.A. De Vore and V.A. Popov, Interpolation of Besov spaces. Trans. Am. Math. Soc. 305 (1988) 397–414. [Google Scholar]
  13. R.A. De Vore and R.C. Sharpley, Besov spaces on domains in ℝd. Trans. Am. Math. Soc. 335 (1993) 843–864. [Google Scholar]
  14. J. Douglas Jr, 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]
  15. S. Duczek and U. Gabbert, Efficient integration method for fictitious domain approaches. Comput. Mech. 56 (2015) 725–738. [Google Scholar]
  16. M.W. Evans and F.H. Harlow, The Particle-in-Cell Method for Hydrodynamic Calculations. Los Alamos National Lab NM (1957). [Google Scholar]
  17. R. Fletcher, Practical Methods of Optimization, 2nd edition. Wiley 7 (2000). [CrossRef] [Google Scholar]
  18. O.H. Hald, Convergence of vortex methods for Euler’s equations. II. SIAM J Numer. Anal. 16 (1979) 726–755. [Google Scholar]
  19. M. Kirchhart and S. Obi, A smooth partition of unity finite element method for vortex particle regularization. SIAM J. Sci. Comput. 39 (2017) A2345–A2364. [Google Scholar]
  20. C. Lehrenfeld, A higher order isoparametric fictitious domain method for level set domains, edited by S.P.A. Bordas, E. Burman, M.G. Larson and M.A. Olshanskii. In: Vol. 121 of Geometrically Unfitted Finite Element Methods and Applications. Lecture Notes in Computational Science and Engineering. Springer (2017) 65–92. [Google Scholar]
  21. Y. Marichal, P. Chatelain and G. Winckelmans, Immersed interface interpolation schemes for particle–mesh methods. J. Comput. Phys. 326 (2016) 947–972. [Google Scholar]
  22. 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 (2014) 604–628. [Google Scholar]
  23. P.-A. Raviart, An analysis of particle methods, edited by F. Brezzi. In: Vol. 1127 of Numerical Methods in Fluid Dynamics. Lecture Notes in Mathematics. Springer (1985) 243–324. [Google Scholar]
  24. L. Rosenhead, The formation of vortices from a surface of discontinuity. Proc. R. Soc. London 142 (1931) 170–192. [Google Scholar]
  25. L.L. Schumaker, Spline Functions. Basic Theory, 3rd edition. Cambridge University Press (2007). [Google Scholar]
  26. B. Seibold, Minimal positive stencils in meshfree finite difference methods for the poisson equation. Comput. Methods Appl. Mech. Eng. 198 (2008) 592–601. [Google Scholar]
  27. S.L. Sobolev and V.L. Vaskevich, The Theory of Cubature Formulas, 1st edition. In: Vol. 415 of Mathematics and Its Appl. Springer (1997). [Google Scholar]
  28. E.M. Stein, Singular Integrals and Differentiability Properties of Functions. In: Vol. 30 of Princeton Mathematical Series. Princeton University Press (1970). [Google Scholar]
  29. V. Tchakaloff, Formules de cubatures mécaniques a coefficients non négatifs. Bull. Sci. Math. 81 (1957) 123–134. [Google Scholar]
  30. M.W. Wilson, A general algorithm for nonnegative quadrature formulas. Math. Comput. 23 (1969) 253–258. [Google Scholar]
  31. R. Yokota, L.A. Barba, T. Narumi and K. Yasuoka, Petascale turbulence simulation using a highly parallel fast multipole method on GPUs. Comput. Phys. Commun. 184 (2013) 445–455. [Google Scholar]

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