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J. Weisz , On an iterative method for the solution of discretized elliptic problems with imperfect contact condition, J. Comput. Appl. Math., 72 (1996), pp. 319–333.
J. R. Barber and R. Zhang , Transient behaviour and stability for the thermoelastic contact of the rods of dissimilar materials, Int. J. Mech. Sci., 30 (1988), pp. 691–704.
C. Peskin and B. Printz , Improved volume conservation in the computation of flows with immersed elastic boundaries, J. Comput. Phys., 105 (1993), pp. 33–46.
M. Sussman , P. Smereka and S. Osher , A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys., 114 (1994), pp. 146–154.
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), pp. 1019–1044.
Z. Li and K. Ito , The Immersed Interface Method: Numerical Solutions of PDES Involving Interfaces and Irregular Domains, SIAM, Philadelphia, 2006.
Z. Li , A fast iterative algorithm for elliptic interface problems, SIAM J. Numer. Anal., 35 (1998), pp. 230–254.
X. Liu , R. P. Fedkiw and M. Kang , A boundary condition capturing method for Poisson's equation on irregular domains, J. Comput. Phys., 160 (2000), pp. 151–178.
R. Fedkiw , T. Aslam , B. Merriman and S. Osher , A non-oscillatory eulerian approach to interfaces in multimaterial flows (the ghost fluid method), J. Comput. Phys., 152 (1999), pp. 457–492.
J.W. L. Wan and X. Liu , A boundary condition capturing multigrid approach to irregular boundary problems, SIAM J. Sci. Comput., 25 (2004), pp. 1982–2003.
P. Macklin and J. S. Lowengrub , A new ghost cell/level set method for moving boundary problems: application to tumor growth, J. Sci. Comput., 35 (2008), pp. 266–299.
Z. Li , T. Lin , Y. Lin and R. Rogers , An immersed finite element space and its approximation capability, Numer. Meth. PDE, 20 (2004), pp. 338–367.
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 (2008), pp. 472–495.
T. Lin , Y. Lin and X. Zhang , Partially penalized immersed finite element methods for elliptic interface problems, SIAM J. Numer. Anal., 53 (2015), pp. 1121–1144.
S. Hou and X. Liu , A numerical method for solving variable coefficient elliptic equations with interfaces, J. Comput. Phys., 202 (2005), pp. 411–445.
S. Hou , W. Wang and L. Wang , Numerical method for solving matrix coefficient elliptic equation with sharp-edged interfaces, J. Comput. Phys., 229 (2010), pp. 7162–7179.
S. Hou , L. Wang and W. Wang , A numerical method for solving the elliptic interface problems with multi-domains and triple junction points, J. Comput. Math, 30 (2012), pp. 504–516.
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), pp. 80–95.
Y. Zhou , S. Zhao , M. Feig and G.W. Wei , High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources, J. Comput. Phys., 213 (2006), pp. 1–30.
S. Yu , Y. Zhou and G. W. Wei , Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces, J. Comput. Phys., 224 (2007), pp. 729–756.
M. Oevermann and R. Klein , A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces, J. Comput. Phys., 219 (2006), pp. 749–769.
M. Oevermann , C. Scharfenberg and R. Klein , A sharp interface finite volume method for elliptic equations on Cartesian grids, J. Comput. Phys., 228 (2009), pp. 5184–5206.
T. Chernogorova , R. E. Ewing , O. Iliev and R. Lazarov , On the discretization of interface problems with perfect and imperfect contact, Lecture Notes in Physics, 552 (2000), pp. 93–103, New York, Springer-Verlag.
Z. Li , T. Lin and X. Wu , New cartesian grid methods for interface problems using the finite element formulation, Numerische Mathematik, 96 (2003), pp. 61–98.