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Volumn 39, Issue 1, 2005, Pages 109-145

Inverted finite elements: A new method for solving elliptic problems in unbounded domains

Author keywords

Inverted elements method; Unbounded domains; Weighted Sobolev spaces

Indexed keywords


EID: 15744375639     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2005001     Document Type: Article
Times cited : (23)

References (36)
  • 1
    • 15744387759 scopus 로고
    • Compact imbeddings of weighted Sobolev spaces on unbounded domains
    • R.A. Adams, Compact imbeddings of weighted Sobolev spaces on unbounded domains. J. Differential Equations 9 (1971) 325-334.
    • (1971) J. Differential Equations , vol.9 , pp. 325-334
    • Adams, R.A.1
  • 4
    • 0030642438 scopus 로고    scopus 로고
    • Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator: An approach in weighted Sobolev spaces
    • C. Amrouche, V. Girault and J. Giroire, Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator: an approach in weighted Sobolev spaces. J. Math. Pures Appl. (9) 76 (1997) 55-81.
    • (1997) J. Math. Pures Appl. (9) , vol.76 , pp. 55-81
    • Amrouche, C.1    Girault, V.2    Giroire, J.3
  • 5
    • 28044459877 scopus 로고
    • A perfectly matched layer for absoption of electromagnetics waves
    • J. Bérenger, A perfectly matched layer for absoption of electromagnetics waves. J. Comput. Physics 114 (1994) 185-200.
    • (1994) J. Comput. Physics , vol.114 , pp. 185-200
    • Bérenger, J.1
  • 6
    • 0029733180 scopus 로고    scopus 로고
    • Perfectly matched layer for the fdtd solution of wave-structure interaction problems
    • J. Bérenger, Perfectly matched layer for the fdtd solution of wave-structure interaction problems. IEEE Trans. Antennas Propagat. 44 (1996) 110-117.
    • (1996) IEEE Trans. Antennas Propagat. , vol.44 , pp. 110-117
    • Bérenger, J.1
  • 7
    • 0017439896 scopus 로고
    • Diffraction and refraction of surface waves using finite and infinite elements
    • P. Bettess and O.C. Zienkiewicz, Diffraction and refraction of surface waves using finite and infinite elements. Internat. J. Numer. Methods Engrg. 11 (1977) 1271-1290.
    • (1977) Internat. J. Numer. Methods Engrg. , vol.11 , pp. 1271-1290
    • Bettess, P.1    Zienkiewicz, O.C.2
  • 9
    • 0037170839 scopus 로고    scopus 로고
    • On the Stokes system and on the biharmonic equation in the half-space: An approach via weighted Sobolev spaces
    • T.Z. Boulmezaoud, On the Stokes system and on the biharmonic equation in the half-space: an approach via weighted Sobolev spaces. Math. Methods Appl. Sci. 25 (2002) 373-398.
    • (2002) Math. Methods Appl. Sci. , vol.25 , pp. 373-398
    • Boulmezaoud, T.Z.1
  • 10
    • 0038189725 scopus 로고    scopus 로고
    • On the Laplace operator and on the vector potential problems in the half-space: An approach using weighted spaces
    • T.Z. Boulmezaoud, On the Laplace operator and on the vector potential problems in the half-space: an approach using weighted spaces. Math. Methods Appl. Sci. 26 (2003) 633-669.
    • (2003) Math. Methods Appl. Sci. , vol.26 , pp. 633-669
    • Boulmezaoud, T.Z.1
  • 11
    • 0028099393 scopus 로고
    • A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion
    • D.S. Burnett, A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion. J. Acoust. Soc. Amer. 96 (1994) 2798-2816.
    • (1994) J. Acoust. Soc. Amer. , vol.96 , pp. 2798-2816
    • Burnett, D.S.1
  • 12
    • 0001039495 scopus 로고
    • Spectral methods for exterior elliptic problems
    • C. Canuto, S.I. Hariharan, L. Lustman, Spectral methods for exterior elliptic problems. Numer. Math. 46 (1985) 505-520.
    • (1985) Numer. Math. , vol.46 , pp. 505-520
    • Canuto, C.1    Hariharan, S.I.2    Lustman, L.3
  • 13
    • 34250247250 scopus 로고
    • s,δ spaces on manifolds which are Euclidean at infinity
    • s,δ spaces on manifolds which are Euclidean at infinity. Acta Math. 146 (1981) 129-150.
    • (1981) Acta Math. , vol.146 , pp. 129-150
    • Choquet-Bruhat, Y.1    Christodoulou, D.2
  • 16
    • 0035583920 scopus 로고    scopus 로고
    • Analysis of a coupled finite-infinite element method for exterior Helmholtz problems
    • L. Demkowicz and F. Ihlenburg, Analysis of a coupled finite-infinite element method for exterior Helmholtz problems. Numer. Math. 88 (2001) 43-73.
    • (2001) Numer. Math. , vol.88 , pp. 43-73
    • Demkowicz, L.1    Ihlenburg, F.2
  • 17
  • 18
    • 0032475723 scopus 로고    scopus 로고
    • A summary of infinite element formulations for exterior Helmholtz problems
    • K. Gerdes, A summary of infinite element formulations for exterior Helmholtz problems. Comput. Methods Appl. Mech. Engrg. 164 (1998) 95-105.
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.164 , pp. 95-105
    • Gerdes, K.1
  • 19
    • 0030286184 scopus 로고    scopus 로고
    • Solution of 3D-Laplace and Helmholtz equations in exterior domains using hp-infinite elements
    • K. Gerdes and L. Demkowicz, Solution of 3D-Laplace and Helmholtz equations in exterior domains using hp-infinite elements. Comput. Methods Appl. Mech. Engrg. 137 (1996) 239-273.
    • (1996) Comput. Methods Appl. Mech. Engrg. , vol.137 , pp. 239-273
    • Gerdes, K.1    Demkowicz, L.2
  • 21
    • 84972539480 scopus 로고
    • The Stokes problem and vector potential operator in three-dimensional exterior domains: An approach in weighted Sobolev spaces
    • V. Girault, The Stokes problem and vector potential operator in three-dimensional exterior domains: an approach in weighted Sobolev spaces. Differential Integral Equations 7 (1994) 535-570.
    • (1994) Differential Integral Equations , vol.7 , pp. 535-570
    • Girault, V.1
  • 23
    • 84966224246 scopus 로고
    • Numerical solution of an exterior Neumann problem using a double layer potential
    • J. Giroire and J.-C. Nédélec, Numerical solution of an exterior Neumann problem using a double layer potential. Math. Comp. 32 (1978) 973-990.
    • (1978) Math. Comp. , vol.32 , pp. 973-990
    • Giroire, J.1    Nédélec, J.-C.2
  • 24
    • 0035616264 scopus 로고    scopus 로고
    • A spectral method for the Stokes problem in three-dimensional unbounded domains
    • electronic
    • L. Halpern, A spectral method for the Stokes problem in three-dimensional unbounded domains. Math. Comp. 70 (2001) 1417-1436 (electronic).
    • (2001) Math. Comp. , vol.70 , pp. 1417-1436
    • Halpern, L.1
  • 25
    • 0000040745 scopus 로고
    • Espaces de Sobolev avec poids application au problème de Dirichlet dans un demi espace
    • B. Hanouzet, Espaces de Sobolev avec poids application au problème de Dirichlet dans un demi espace. Rend. Sem. Mat. Univ. Padova 46 (1971) 227-272.
    • (1971) Rend. Sem. Mat. Univ. Padova , vol.46 , pp. 227-272
    • Hanouzet, B.1
  • 26
    • 0003543733 scopus 로고
    • Cambridge Mathematical Library. Cambridge University Press, Cambridge
    • G.H. Hardy, J.E. Littlewood and G. Pólya, Inequalities. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1988).
    • (1988) Inequalities
    • Hardy, G.H.1    Littlewood, J.E.2    Pólya, G.3
  • 27
    • 0346194172 scopus 로고
    • Sur la complétion par rapport à une intégrale de Dirichlet
    • L. Hörmander and J.L. Lions, Sur la complétion par rapport à une intégrale de Dirichlet. Math. Scand. 4 (1956) 259-270.
    • (1956) Math. Scand. , vol.4 , pp. 259-270
    • Hörmander, L.1    Lions, J.L.2
  • 28
    • 0003691880 scopus 로고    scopus 로고
    • Finite element analysis of acoustic scattering, Springer-Verlag, New York
    • F. Ihlenburg, Finite element analysis of acoustic scattering, volume 132 of Applied Mathematical Sciences. Springer-Verlag, New York (1998).
    • (1998) Applied Mathematical Sciences , vol.132
    • Ihlenburg, F.1
  • 29
    • 0000309125 scopus 로고
    • Boundary value problems for elliptic equations in domains with conical or angular points
    • V.A. Kondratev, Boundary value problems for elliptic equations in domains with conical or angular points. Trudy Moskov. Mat. Obvsvc. 16 (1967) 209-292.
    • (1967) Trudy Moskov. Mat. Obvsvc. , vol.16 , pp. 209-292
    • Kondratev, V.A.1
  • 30
    • 0003440536 scopus 로고
    • A Wiley-Interscience Publication. John Wiley & Sons Inc., New York
    • A. Kufner, Weighted Sobolev spaces. A Wiley-Interscience Publication. John Wiley & Sons Inc., New York (1985).
    • (1985) Weighted Sobolev Spaces
    • Kufner, A.1
  • 32
    • 0017732003 scopus 로고
    • Méthode d'éléments finis pour la résolution numérique de problèmes extérieurs en dimension 2
    • M.N. Le Roux, Méthode d'éléments finis pour la résolution numérique de problèmes extérieurs en dimension 2. RAIRO Anal. Numér. 11 (1977) 27-60.
    • (1977) RAIRO Anal. Numér. , vol.11 , pp. 27-60
    • Le Roux, M.N.1
  • 33
    • 15744361957 scopus 로고
    • Weighted spaces with inhomogeneous norms, and boundary value problems in domains with conical points
    • Wilhelm-Pieck-Univ. Rostock
    • V.G. Maz'ya and B.A. Plamenevskii, Weighted spaces with inhomogeneous norms, and boundary value problems in domains with conical points, in Elliptische Differentialgleichungen (Meeting, Rostock, 1977). Wilhelm-Pieck-Univ. Rostock (1978) 161-190.
    • (1978) Elliptische Differentialgleichungen (Meeting, Rostock, 1977) , pp. 161-190
    • Maz'ya, V.G.1    Plamenevskii, B.A.2
  • 36
    • 0020764338 scopus 로고
    • Solution of acoustic scattering problems by means of second kind integral equations
    • V. Rokhlin, Solution of acoustic scattering problems by means of second kind integral equations. Wave Motion 5 (1983) 257-272.
    • (1983) Wave Motion , vol.5 , pp. 257-272
    • Rokhlin, V.1


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