[1] |
Zhiming, Chen; Jun, Zou: Finite element methods and their convergence for elliptic and parabolic interface problems. Numerische Mathematik 79, 175-202 (1998) · Zbl 0909.65085 |

[2] |
Fedkiw, R.; Aslam, T.; Merriman, B.; Osher, S.: A non-oscillatory Eulerian approach to interfaces in multimaterial flows (The ghost fluid method). J. comput. Phys. 152, No. 2, 457-492 (1999) · Zbl 0957.76052 |

[3] |
Gibou, F.; Fedkiw, R.; Cheng, L. -T.; Kang, M. A.: Second order accurate symmetric discretization of the Poisson equation on irregular domains. J. comput. Phys. 176, 1-23 (2002) · Zbl 0996.65108 |

[4] |
P. Grisvard, Elliptic problems in nonsmooth domains - Monographs and Studies in Mathematics, Pitman Advanced Publishing Program. ISSN 0743-0329, 1985 · Zbl 0695.35060 |

[5] |
Leveque, R. J.; Li, Z.: The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. anal. 31, 1019 (1994) · Zbl 0811.65083 |

[6] |
Li, Z.: A fast iterative algorithm for elliptic interface problems. SIAM J. Numer. anal. 35, No. 1, 230-254 (1998) · Zbl 0915.65121 |

[7] |
Z. Li, T. Lin, X. Wu, New Cartesian grid methods for interface problems using the finite element formulation, Numerische Mathematik, 9661-98, (2003). Preprint. NCSU CRSC-TR99-12 · Zbl 1055.65130 |

[8] |
Liu, Xu-Dong; Fedkiw, Ronald P.; Kang, Myungjoo: A boundary condition capturing method for Poisson’s equation on irregular domains. J. comput. Phys. 160, No. 1, 151-178 (2000) · Zbl 0958.65105 |

[9] |
Liu, X. -D.; Sideris, T.: Convergence of the ghost fluid method for elliptic equations with interfaces. Math. comp. 72 (2003) · Zbl 1027.65140 |

[10] |
Mayo, A.: The fast solution of Poisson’s and the biharmonic equations in irregular domains. SIAM J. Numer. anal. 21, No. 2, 285-299 (1984) · Zbl 1131.65303 |

[11] |
Mayo, A.: Fast high order accurate solutions of Laplace’s equation on irregular domains. SIAM J. Sci. stat. Comput. 6, No. 1, 144-157 (1985) · Zbl 0559.65082 |

[12] |
J. Necas, Introduction to the theory of nonlinear elliptic equations, Teubner-Texte zur Mathematik. Band 52, ISSN 0138-502X, 1983 |

[13] |
Peskin, C.: Numerical analysis of blood flow in the heart. J. comput. Phys. 25, 220-252 (1977) · Zbl 0403.76100 |

[14] |
Peskin; C.; ; Printz, B.: Improved volume conservation in the computation of flows with immersed elastic boundaries. J. comput. Phys. 105, 33-46 (1993) · Zbl 0762.92011 |

[15] |
Sussman, M.; Smereka, P.; Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. comput. Phys. 114, 146-154 (1994) · Zbl 0808.76077 |

[16] |
Wan, Justin W. L.; Liu, Xu-Dong: A boundary condition capturing multigrid approach to irregular boundary problems. SIAM J. Sci. comput. 25, No. 6, 1982-2003 (2004) · Zbl 1107.65032 |