참고문헌
- I. Babuska, The finite element method for elliptic equations with discontinuous coefficients, Computing 5 (1970), 207-213. https://doi.org/10.1007/BF02248021
- J. W. Barrett and C. M. Elliott, Fitted and unfitted finite-element methods for elliptic equations with smooth interfaces, IMA J. Numer. Anal. 7 (1987), no. 3, 283-300. https://doi.org/10.1093/imanum/7.3.283
- J. H. Bramble and J. T. King, A finite element method for interface problems in domains with smooth boundaries and interfaces, Adv. Comput. Math. 6 (1996), no. 2, 109-138. https://doi.org/10.1007/BF02127700
- S. C. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods, Springer-Verlag, New York, 1994.
- C. M. Chen and V. Thomee, The lumped mass finite element method for a parabolic problems, J. Austral. Math. Soc. Ser. B 26 (1985), no. 3, 329-354. https://doi.org/10.1017/S0334270000004549
- Z. Chen and J. Zou, Finite element methods and their convergence for elliptic and parabolic interface problems, Numer. Math. 79 (1998), no. 2, 175-202. https://doi.org/10.1007/s002110050336
- P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North Holland, Amsterdam, 1975.
- B. Deka, Finite element methods with numerical quadrature for elliptic problems with smooth interfaces, J. Comput. Appl. Math. 234 (2010), no. 2, 605-612. https://doi.org/10.1016/j.cam.2009.12.052
- B. Deka and T. Ahmed, Semidiscrete finite element methods for linear and semilinear parabolic problems with smooth interfaces: some new optimal error estimates, Numer. Funct. Anal. Optim. 33 (2012), no. 5, 524-544. https://doi.org/10.1080/01630563.2011.651189
-
B. Deka and R. K. Sinha,
$L^{\infty}(L^2)$ and$L^{\infty}(H^1)$ norms error estimates in finite element method for linear parabolic interface problems, Numer. Funct. Anal. Optim. 32 (2011), no. 3, 267-285. https://doi.org/10.1080/01630563.2010.532272 - B. Deka, R. K. Sinha, R. C. Deka, and T. Ahmed, Finite element method with quadrature for parabolic interface problems, Neural Parallel Sci. Comput. 21 (2013), no. 3-4, 477-496.
- H. Duan, P. Lin, and Roger C. E. Tan, Analysis of a continuous finite element method for H(curl, div)-elliptic interface problem, Numer. Math. 123 (2013), no. 4, 671-707. https://doi.org/10.1007/s00211-012-0500-x
- A. Hansbo and P. Hansbo, An unfitted finite element method, based on Nitsche's method, for elliptic interface problems, Comput. Methods Appl. Mech. Engrg. 191 (2002), no. 47-48, 5537-5552. https://doi.org/10.1016/S0045-7825(02)00524-8
- J. Huang and J. Zou, A mortar element method for elliptic problems with discontinuous coefficients, IMA J. Numer. Anal. 22 (2002), no. 4, 554-576.
- J. Huang and J. Zou, Some new a priori estimates for second-order elliptic and parabolic interface problems, J. Differential Equations 184 (2002), no. 2, 570-586. https://doi.org/10.1006/jdeq.2001.4154
- M. Kumar and P. Joshi, Some numerical techniques for solving elliptic interface problems, Numer. Methods Partial Differential Equations 28 (2012), no. 1, 94-114. https://doi.org/10.1002/num.20609
- O. A. Ladyzhenskaya, V. Ja. Rivkind, and N. N. Ural'ceva, The classical solvability of diffraction problems, Trudy Mat. Inst. Steklov 92 (1966), 116-146.
- J. Li, J. M. Melenk, B. Wohlmuth, and J. Zou, Optimal a priori estimates for higher order finite elements for elliptic interface problems, Appl. Numer. Math. 60 (2010), no. 1-2, 19-37. https://doi.org/10.1016/j.apnum.2009.08.005
- R. Massjung, An unfitted discontinuous Galerkin method applied to elliptic interface problems, SIAM J. Numer. Anal. 50 (2012), no. 6, 3134-3162. https://doi.org/10.1137/090763093
- B. F. Nielsen, Finite element discretizations of elliptic problems in the presence of arbitrarily small ellipticity: An error analysis, SIAM J. Numer. Anal. 36 (1999), no. 2, 368-392. https://doi.org/10.1137/S0036142997319431
- P. A. Raviart, The Use of Numerical Integration in Finite Element Methods for Solving Parabolic Equations, Topics in numerical analysis (Proc. Roy. Irish Acad. Conf., University Coll., Dublin, 1972), pp. 233-264. Academic Press, London, 1973.
- R. K. Sinha and B. Deka, Optimal error estimates for linear parabolic problems with discontinuous coefficients, SIAM J. Numer. Anal. 43 (2005), no. 2, 733-749. https://doi.org/10.1137/040605357
- R. K. Sinha and B. Deka, A priori error estimates in the finite element method for nonself-adjoint elliptic and parabolic interface problems, Calcolo 43 (2006), no. 4, 253-278. https://doi.org/10.1007/s10092-006-0122-8
- V. Thomee, Galerkin Finite Element Methods for Parabolic Problems, Springer-Verlag, 1997.
피인용 문헌
- Weak Galerkin Finite Element Methods for Parabolic Interface Problems with Nonhomogeneous Jump Conditions pp.1532-2467, 2019, https://doi.org/10.1080/01630563.2018.1549074