Free Access
Volume 50, Number 5, September-October 2016
Page(s) 1561 - 1583
Published online 20 September 2016
  1. S. Adjerid, M. Ben-Romdhane and T. Lin, Higher degree immersed finite element methods for second-order elliptic interface problems. Int. J. Numer. Anal. Model. 11 (2014) 541–566. [MathSciNet] [Google Scholar]
  2. C. Annavarapu, M. Hautefeuille and J.E. Dolbow, A robust Nitsche’s formulation for interface problems. Comput. Methods Appl. Mech. Engrg. 225/228 (2012) 44–54. [CrossRef] [Google Scholar]
  3. J.T. Beale and A.T. Layton, On the accuracy of finite difference methods for elliptic problems with interfaces. Commun. Appl. Math. Comput. Sci. 1 (2006) 91–119. [CrossRef] [MathSciNet] [Google Scholar]
  4. J. Bedrossian, J.H. von Brecht, S. Zhu, E. Sifakis and J.M. Teran, A second order virtual node method for elliptic problems with interfaces and irregular domains. J. Comput. Phys. 229 (2010) 6405–6426. [CrossRef] [MathSciNet] [Google Scholar]
  5. D. Boffi and L. Gastaldi, A finite element approach for the immersed boundary method. Comput. Struct. 81 (2003) 491–501. In honour of Klaus-Jürgen Bathe. [CrossRef] [Google Scholar]
  6. D. Boffi, N. Cavallini and L. Gastaldi, Finite element approach to immersed boundary method with different fluid and solid densities. Math. Models Methods Appl. Sci. 21 (2011) 2523–2550. [CrossRef] [MathSciNet] [Google Scholar]
  7. S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods. Vol. 15 of Texts in Applied Mathematics. Springer-Verlag, New York (1994). [Google Scholar]
  8. E. Burman, Ghost penalty. C. R. Math. Acad. Sci. Paris 348 (2010) 1217–1220. [CrossRef] [MathSciNet] [Google Scholar]
  9. E. Burman, Projection stabilization of Lagrange multipliers for the imposition of constraints on interfaces and boundaries. Numer. Methods Partial Differ. Equ. 30 (2014) 567–592. [CrossRef] [Google Scholar]
  10. E. Burman and P. Hansbo, Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method. Comput. Methods Appl. Mech. Engrg. 199 (2010) 2680–2686. [Google Scholar]
  11. 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. [CrossRef] [MathSciNet] [Google Scholar]
  12. E. Burman and P. Zunino, Numerical approximation of large contrast problems with the unfitted Nitsche method. In Frontiers in numerical analysis – Durham 2010. Vol. 85 of Lect. Notes Comput. Sci. Eng. Springer, Heidelberg (2012) 227–282. [Google Scholar]
  13. C.-C. Chu, I.G. Graham and T.-Y. Hou, A new multiscale finite element method for high-contrast elliptic interface problems. Math. Comput. 79 (2010) 1915–1955. [CrossRef] [Google Scholar]
  14. R. Cortez, L. Fauci, N. Cowen and R. Dillon, Simulation of swimming organisms: Coupling internal mechanics with external fluid dynamics. Comput. Sci. Eng. 6 (2004) 38–45. [CrossRef] [Google Scholar]
  15. A. Demlow, D. Leykekhman, A.H. Schatz and L.B. Wahlbin, Best approximation property in the Formula norm for finite element methods on graded meshes. Math. Comput. 81 (2012) 743–764. [CrossRef] [Google Scholar]
  16. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Classics in Mathematics. Reprint of the 1998 edition. Springer-Verlag, Berlin (2001). [Google Scholar]
  17. V. Girault, R.H. Nochetto and R. Scott, Stability of the finite element Stokes projection in W1,. C. R. Math. Acad. Sci. Paris 338 (2004) 957–962. [CrossRef] [MathSciNet] [Google Scholar]
  18. Y. Gong, B. Li and Z. Li, Immersed-interface finite-element methods for elliptic interface problems with nonhomogeneous jump conditions. SIAM J. Numer. Anal. 46 (2007/08) 472–495. [CrossRef] [MathSciNet] [Google Scholar]
  19. J. Guzmán and D. Leykekhman, Pointwise error estimates of finite element approximations to the Stokes problem on convex polyhedra. Math. Comput. 81 (2012) 1879–1902. [CrossRef] [Google Scholar]
  20. X. He, T. Lin and Y. Lin, Immersed finite element methods for elliptic interface problems with non-homogeneous jump conditions. Int. J. Numer. Anal. Model. 8 (2011) 284–301. [MathSciNet] [Google Scholar]
  21. S. Hou and X.-D. Liu, A numerical method for solving variable coefficient elliptic equation with interfaces. J. Comput. Phys. 202 (2005) 411–445. [CrossRef] [MathSciNet] [Google Scholar]
  22. S. Hou, W. Wang and L. Wang, Numerical method for solving matrix coefficient elliptic equation with sharp-edged interfaces. J. Comput. Phys. 229 (2010) 7162–7179. [CrossRef] [MathSciNet] [Google Scholar]
  23. S. Hou, P. Song, L. Wang and H. Zhao, A weak formulation for solving elliptic interface problems without body fitted grid. J. Comput. Phys. 249 (2013) 80–95. [CrossRef] [MathSciNet] [Google Scholar]
  24. M. Sanchez-Uribe, J. Guzman and M. Sarkis, On the accuracy of finite element approximations to a class of interface problems. Technical Report 2014-6, Scientific Computing Group, Brown University, Providence, RI, USA, March (2014). [Google Scholar]
  25. L. Lee and R.J. Leveque, An immersed interface method for incompressible Navier-Stokes equations. SIAM J. Sci. Comput. 25 (2003) 832–856. [CrossRef] [MathSciNet] [Google Scholar]
  26. R.J. LeVeque and Z.L. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31 (1994) 1019–1044. [CrossRef] [MathSciNet] [Google Scholar]
  27. R.J. LeVeque and Z. Li, Immersed interface methods for Stokes flow with elastic boundaries or surface tension. SIAM J. Sci. Comput. 18 (1997) 709–735. [CrossRef] [MathSciNet] [Google Scholar]
  28. Z. Li and M.-C. Lai, The immersed interface method for the Navier–Stokes equations with singular forces. J. Comput. Phys. 171 (2001) 822–842. [CrossRef] [MathSciNet] [Google Scholar]
  29. A.N. Marques, J.-C. Nave and R.R. Rosales, A correction function method for Poisson problems with interface jump conditions. J. Comput. Phys. 230 (2011) 7567–7597. [CrossRef] [MathSciNet] [Google Scholar]
  30. C.S. Peskin, Numerical analysis of blood flow in the heart. J. Comput. Phys. 25 (1977) 220–252. [CrossRef] [Google Scholar]
  31. C.S. Peskin, The immersed boundary method. Acta Numer. 11 (2002) 479–517. [CrossRef] [MathSciNet] [Google Scholar]
  32. R. Rannacher and R. Scott, Some optimal error estimates for piecewise linear finite element approximations. Math. Comput. 38 (1982) 437–445. [CrossRef] [MathSciNet] [Google Scholar]
  33. P.-A. Raviart and J.M. Thomas, A mixed finite element method for 2nd order elliptic problems. In Mathematical aspects of finite element methods (Proc. Conf., Consiglio Naz. delle Ricerche, C.N.R., Rome, 1975). Vol. 606 of Lect. Notes Math. Springer, Berlin (1977) 292–315. [Google Scholar]
  34. C. Tu and C.S. Peskin, Stability and instability in the computation of flows with moving immersed boundaries: a comparison of three methods. SIAM J. Sci. Statist. Comput. 13 (1992) 1361–1376. [CrossRef] [MathSciNet] [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