Free access
Issue
ESAIM: M2AN
Volume 45, Number 4, July-August 2011
Page(s) 651 - 674
DOI http://dx.doi.org/10.1051/m2an/2010069
Published online 30 November 2010
  1. R.A. Adams and J.J.F. Fournier, Sobolev spaces. Academic Press (2003).
  2. J.H. Bramble and J.T. King, A robust finite element method for nonhomogeneous Dirichlet problems in domains with curved boundaries. Math. Comp. 63 (1994) 1–17. [CrossRef] [MathSciNet]
  3. F. Brezzi, J. Douglas and L.D. Marini, Two families of mixed finite elements for second order elliptic problems. Numer. Math. 47 (1985) 217–235. [CrossRef] [MathSciNet]
  4. F. Brezzi, G. Manzini, L.D. Marini, P. Pietra and A. Russo, Discontinuous galerkin approximations for elliptic problems. Numer. Methods Partial Differ. Equ. 16 (2000) 365–378. [CrossRef] [MathSciNet]
  5. F. Brezzi, T.J.R. Hughes, L.D. Marini and A. Masud, Mixed discontinuous Galerkin methods for Darcy flow. J. Sci. Comput. 22 (2005) 119–145. [CrossRef] [MathSciNet]
  6. E. Burman and P. Hansbo, Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method. Comput. Methods Appl. Mech. Eng. 199 (2010) 2680–2686. [CrossRef] [MathSciNet]
  7. P.G. Ciarlet, The finite element method for elliptic problems. North-Holland (1978).
  8. R. Codina and J. Baiges, Approximate imposition of boundary conditions in immersed boundary methods. Int. J. Numer. Methods Eng. 80 (2009) 1379–1405. [CrossRef]
  9. A. Ern and J.L. Guermond, Theory and practice of finite elements. Springer-Verlag (2004).
  10. L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions. CRC (1992).
  11. V. Girault and R. Glowinski, Error analysis of a fictitious domain method applied to a Dirichlet problem. Japan J. Indust. Appl. Math. 12 (1995) 487–514. [CrossRef] [MathSciNet]
  12. R. Glowinski, T.W. Pan and J. Periaux, A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Eng. 111 (1994) 283–303. [CrossRef] [MathSciNet]
  13. A. Hansbo and P. Hansbo, An unfitted finite element method, based on Nitsche's method, for elliptic interface problems. Comput. Methods Appl. Mech. Eng. 191 (2002) 5537–5552. [CrossRef] [MathSciNet]
  14. D. Henry, J. Hale and A.L. Pereira, Perturbation of the boundary in boundary-value problems of partial differential equations. Cambridge University Press, Cambridge (2005).
  15. M. Lenoir, Optimal isoparametric finite elements and error estimates for domains involving curved boundaries. SIAM J. Numer. Anal. 23 (1986) 562–580. [CrossRef] [MathSciNet]
  16. R.J. Leveque and Z. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31 (1994) 1019–1044. [CrossRef] [MathSciNet]
  17. A.J. Lew and G.C. Buscaglia, A discontinuous-Galerkin-based immersed boundary method. Int. J. Numer. Methods Eng. 76 (2008) 427–454. [CrossRef]
  18. A. Lew, P. Neff, D. Sulsky and M. Ortiz, Optimal BV estimates for a discontinuous Galerkin method in linear elasticity. Appl. Math. Res. Express 3 (2004) 73–106. [CrossRef]
  19. J.L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. Springer-Verlag (1972).
  20. J. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind, in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 36, Springer (1971) 9–15.
  21. R. Rangarajan, A. Lew and G.C. Buscaglia, A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity. Comput. Methods Appl. Mech. Eng. 198 (2009) 1513–1534. [CrossRef]
  22. V. Thomee, Polygonal domain approximation in Dirichlet's problem. J. Inst. Math. Appl. 11 (1973) 33–44. [CrossRef] [MathSciNet]

Recommended for you