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Volumn 60, Issue 1-2, 2010, Pages 19-37

Optimal a priori estimates for higher order finite elements for elliptic interface problems

Author keywords

A priori estimates; Elliptic interface problems; Higher order finite elements; Optimal convergence rates

Indexed keywords

A-PRIORI ESTIMATES; ELLIPTIC INTERFACE PROBLEMS; FINITE ELEMENT; HIGHER ORDER; OPTIMAL CONVERGENCE;

EID: 71549123189     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2009.08.005     Document Type: Article
Times cited : (190)

References (27)
  • 1
    • 0003796630 scopus 로고
    • Academic Press, New York/London
    • Adams R.A. Sobolev Spaces (1975), Academic Press, New York/London
    • (1975) Sobolev Spaces
    • Adams, R.A.1
  • 2
    • 0000024779 scopus 로고
    • The finite element method for elliptic equations with discontinuous coefficients
    • Babuška I. The finite element method for elliptic equations with discontinuous coefficients. Computing 5 (1970) 207-213
    • (1970) Computing , vol.5 , pp. 207-213
    • Babuška, I.1
  • 3
    • 0011914559 scopus 로고
    • Fitted and unfitted finite-element methods for elliptic equations with smooth interfaces
    • Barrett J.W., and Elliott C.M. Fitted and unfitted finite-element methods for elliptic equations with smooth interfaces. IMA J. Numer. Anal. 7 (1987) 283-300
    • (1987) IMA J. Numer. Anal. , vol.7 , pp. 283-300
    • Barrett, J.W.1    Elliott, C.M.2
  • 4
    • 21444439361 scopus 로고    scopus 로고
    • A finite element method for interface problems in domains with smooth boundaries and interfaces
    • Bramble J.H., and King J.T. A finite element method for interface problems in domains with smooth boundaries and interfaces. Adv. Comput. Math. 6 (1996) 109-138
    • (1996) Adv. Comput. Math. , vol.6 , pp. 109-138
    • Bramble, J.H.1    King, J.T.2
  • 6
    • 85120507199 scopus 로고    scopus 로고
    • E. Burman, P. Hansbo, Interior penalty stabilized Lagrange multiplier methods for the finite element solution of elliptic interface problems, Preprint, Finite Element Center, 2007. IMA Journal of Numerical Analysis, in press, doi: 10.1093/imanum/drn081
    • E. Burman, P. Hansbo, Interior penalty stabilized Lagrange multiplier methods for the finite element solution of elliptic interface problems, Preprint, Finite Element Center, 2007. IMA Journal of Numerical Analysis, in press, doi: 10.1093/imanum/drn081
  • 7
    • 33645794314 scopus 로고    scopus 로고
    • Quadratic immersed finite element spaces and their approximation capabilities
    • Camp B., Lin T., Lin Y., and Su W. Quadratic immersed finite element spaces and their approximation capabilities. Adv. Comput. Math. 24 (2006) 81-112
    • (2006) Adv. Comput. Math. , vol.24 , pp. 81-112
    • Camp, B.1    Lin, T.2    Lin, Y.3    Su, W.4
  • 8
    • 0032396367 scopus 로고    scopus 로고
    • Finite element methods and their convergence for elliptic and parabolic interface problems
    • Chen Z., and Zou J. Finite element methods and their convergence for elliptic and parabolic interface problems. Numer. Math. 79 (1998) 175-202
    • (1998) Numer. Math. , vol.79 , pp. 175-202
    • Chen, Z.1    Zou, J.2
  • 9
    • 0003204969 scopus 로고
    • The Finite Element Method for Elliptic Problems
    • North-Holland Pub. Co., Amsterdam/New York
    • Ciarlet P.G. The Finite Element Method for Elliptic Problems. Studies in Mathematics and its Applications. first ed. (1978), North-Holland Pub. Co., Amsterdam/New York
    • (1978) Studies in Mathematics and its Applications. first ed.
    • Ciarlet, P.G.1
  • 10
    • 0016541865 scopus 로고
    • Approximation by finite element functions using local regularization
    • Clément P. Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 2 (1975) 77-84
    • (1975) RAIRO Anal. Numér. , vol.2 , pp. 77-84
    • Clément, P.1
  • 11
    • 0000277324 scopus 로고
    • Blending-function methods of bivariate and multivariate interpolation and approximation
    • Gordon W.J. Blending-function methods of bivariate and multivariate interpolation and approximation. SIAM J. Numer. Anal. 8 1 (1971) 158-177
    • (1971) SIAM J. Numer. Anal. , vol.8 , Issue.1 , pp. 158-177
    • Gordon, W.J.1
  • 12
    • 84985315986 scopus 로고
    • Construction of curvilinear coordinate systems and application to mesh generation
    • Gordon W.J., and Hall C.A. Construction of curvilinear coordinate systems and application to mesh generation. Int. J. Numer. Meth. Eng. 7 (1973) 461-477
    • (1973) Int. J. Numer. Meth. Eng. , vol.7 , pp. 461-477
    • Gordon, W.J.1    Hall, C.A.2
  • 13
    • 0000686693 scopus 로고
    • Transfinite element methods: Blending-function interpolation over arbitrary curved element domains
    • Gordon W.J., and Hall C.A. Transfinite element methods: Blending-function interpolation over arbitrary curved element domains. Numer. Math. 21 2 (1973) 109-129
    • (1973) Numer. Math. , vol.21 , Issue.2 , pp. 109-129
    • Gordon, W.J.1    Hall, C.A.2
  • 15
    • 0037159814 scopus 로고    scopus 로고
    • An unfitted finite element method, based on Nitsche's method, for elliptic interface problems
    • Hansbo A., and Hansbo P. An unfitted finite element method, based on Nitsche's method, for elliptic interface problems. Comput. Meth. Appl. Mech. Eng. 191 47 (2002) 537-552
    • (2002) Comput. Meth. Appl. Mech. Eng. , vol.191 , Issue.47 , pp. 537-552
    • Hansbo, A.1    Hansbo, P.2
  • 16
    • 0036035450 scopus 로고    scopus 로고
    • A mortar element method for elliptic problems with discontinuous coefficients
    • Huang J., and Zou J. A mortar element method for elliptic problems with discontinuous coefficients. IMA J Numer. Anal. 22 (2002) 549-576
    • (2002) IMA J Numer. Anal. , vol.22 , pp. 549-576
    • Huang, J.1    Zou, J.2
  • 17
    • 0022734898 scopus 로고
    • Optimal isoparametric finite elements and error estimates for domains involving curved boundaries
    • Lenoir M. Optimal isoparametric finite elements and error estimates for domains involving curved boundaries. SIAM J. Numer. Anal. 23 (1986) 562-580
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 562-580
    • Lenoir, M.1
  • 19
    • 0742271742 scopus 로고    scopus 로고
    • New Cartesian grid methods for interface problem using finite element formulation
    • Li Z., Lin T., and Wu X. New Cartesian grid methods for interface problem using finite element formulation. Numer. Math. 96 (2003) 61-98
    • (2003) Numer. Math. , vol.96 , pp. 61-98
    • Li, Z.1    Lin, T.2    Wu, X.3
  • 20
    • 34250821173 scopus 로고    scopus 로고
    • Error estimation of a class of quadratic immersed finite element methods for elliptic interface problems
    • Lin T., Lin Y., and Sun W. Error estimation of a class of quadratic immersed finite element methods for elliptic interface problems. Disc. Cont. Dynam. Sys. Series B 7 4 (2007) 807-823
    • (2007) Disc. Cont. Dynam. Sys. Series B , vol.7 , Issue.4 , pp. 807-823
    • Lin, T.1    Lin, Y.2    Sun, W.3
  • 21
    • 0242308001 scopus 로고    scopus 로고
    • Optimal a priori estimates for interface problems
    • Plum M., and Wieners C. Optimal a priori estimates for interface problems. Numer. Math. 95 (2003) 735-759
    • (2003) Numer. Math. , vol.95 , pp. 735-759
    • Plum, M.1    Wieners, C.2
  • 22
    • 84966200902 scopus 로고
    • Finite element interpolation of nonsmooth functions satisfying boundary conditions
    • Scott L.R., and Zhang Z. Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483-493
    • (1990) Math. Comp. , vol.54 , pp. 483-493
    • Scott, L.R.1    Zhang, Z.2
  • 24
    • 0035860267 scopus 로고    scopus 로고
    • Modeling holes and inclusions by level sets in the extended finite-element method
    • Sukumar N., Chopp D.L., Noës N., and Bleytschko T. Modeling holes and inclusions by level sets in the extended finite-element method. Comput. Meth. Appl. Mech. Eng. 190 (2001) 6183-6200
    • (2001) Comput. Meth. Appl. Mech. Eng. , vol.190 , pp. 6183-6200
    • Sukumar, N.1    Chopp, D.L.2    Noës, N.3    Bleytschko, T.4
  • 25
    • 67650048440 scopus 로고    scopus 로고
    • An Introduction to Sobolev Spaces and Interpolation Spaces
    • Springer, Berlin
    • Tartar L. An Introduction to Sobolev Spaces and Interpolation Spaces. Lecture Notes of the Unione Matematica Italiana vol. 3 (2007), Springer, Berlin
    • (2007) Lecture Notes of the Unione Matematica Italiana , vol.3
    • Tartar, L.1


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