| [1] Li J, Renardy Y, Renardy M. Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method[J]. Physics of Fluids, 2000, 12(2):269-282.[2] Hetzer G, Meir A. On an interface problem with a nonlinear jump condition, numerical approximation of solutions[J]. International Journal of Numerical Analysis and Modeling, 2007, 4(3-4):519-530.[3] Babuška I. The finite element method for elliptic equations with discontinuous coefficients[J]. Computing, 1970, 5(3):207-213.[4] He X, Lin T, Lin Y. Immersed finite element methods for elliptic interface problems with nonhomogeneous jump conditions[J]. International Journal of Numerical Analysis and Modeling, 2011, 8(2):284-301.[5] He X, Lin T, Lin Y. The convergence of the bilinear and linear immersed finite element solutions to interface problems[J]. Numerical Methods for Partial Differential Equations, 2012, 28(1):312-330.[6] Zhang Q, Ito K, Li Z, Zhang Z. Immersed finite elements for optimal control problems of elliptic PDEs with interfaces[J]. Journal of Computational Physics, 2015, 298(C):305-319.[7] Han H. The numerical solutions of interface problems by infinite element method[J]. Numerische Mathematik, 1982, 39(1):39-50.[8] Barrett J, Elliott C. Fitted and unfitted finite-element methods for elliptic equations with smooth interfaces[J]. IMA Journal of Numerical Analysis, 1987, 7(3):283-300.[9] Chen Z, Zou J. Finite element methods and their convergence for elliptic and parabolic interface problems[J]. Numerische Mathematik, 1998, 79(2):175-202.[10] Guan H, Shi D. P1-nonconforming triangular FEM for elliptic and parabolic interface problems[J]. Applied Mathematics and Mechanics, 2015, 36(9) 1197-1212.[11] Sinha R, Deka B. A priori error estimates in the finite element method for nonself-adjoint elliptic and parabolic interface problems[J]. Calcolo, 2006, 43(4):253-278.[12] Sinha R, Deka B. Finite element methods for semilinear elliptic and parabolic interface problems[J]. Applied Numerical Mathematics, 2009, 59(8):1870-1883.[13] Huang J, Zou J. Some New a priori estimates for second-order elliptic and parabolic interface problems[J]. Journal of Differential Equations, 2002, 184(2):570-586.[14] Li J, Melenk J, Wohlmuth B, Zou J. Optimal a priori estimates for higher order finite elements for elliptic interface problems[J]. Applied Numerical Mathematics, 2010, 60(1-2):19-37.[15] 梁国平．变网格的有限元法[J]．计算数学, 1985, 11(4):377-384[16] 袁益让. 一类退化非线性抛物型方程组的变网格有限元方法[J]. 计算数学, 1986, 12(2):121-136[17] Shi D, Zhang Y. A nonconforming anisotropic finite element approximation with moving grids for stokes problem[J]. Journal of Computational Mathematics, 2007, 24(5):561-578.[18] Shi D, Guan H. A class of Crouzeix-Raviart type nonconforming finite element methods for parabolic variational inequality problem with moving grid on anisotropic meshes[J]. Hokkaido Mathematical Journal, 2007, 36(4):687-709.[19] Brenner S, Scott L. The Mathematical Theory of Finite Element Methods[M]. Springer-Verlag, Berlin, 1994.[20] Attanayake C, Senaratne D. Convergence of an immersed finite element method for semilinear parabolic interface problems[J]. Applied Mathematical Sciences, 2011, 5(3):135-147.[21] Thomas A, Serge N, Joachim S. Crouzeix-Raviart type finite elements on anisotropic meshes[J]. Numerische Mathematik, 2001, 89(2):193-223.[22] Kim S, Yim J, Sheen D. Stable cheapest nonconforming finite elements for the Stokes equations[J]. Journal of Computational and Applied Mathematics, 2016, 299:2-14. |
