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Volumn 21, Issue 9, 1998, Pages 823-864

Vector potentials in three-dimensional non-smooth domains

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; FUNCTIONS; VISCOUS FLOW;

EID: 0032097489     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1476(199806)21:9<823::AID-MMA976>3.0.CO;2-B     Document Type: Article
Times cited : (784)

References (35)
  • 1
    • 11744358938 scopus 로고
    • Academic Press, New York
    • Adams, R. A., Soboler Spaces, Academic Press, New York, 1975.
    • (1975) Soboler Spaces
    • Adams, R.A.1
  • 2
    • 84980080664 scopus 로고
    • Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
    • Agmon, S., Douglis, A. and Nirenberg, L., 'Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II', Comm. Pure Appl. Math., 17, 35-92 (1964)
    • (1964) Comm. Pure Appl. Math. , vol.17 , pp. 35-92
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 3
    • 0009964350 scopus 로고
    • Potential representation of incompressible vector fields
    • SIAM, Philadelphia
    • Auchmuty, G., 'Potential representation of incompressible vector fields', in: Nonlinear Problems in Applied Mathematics, SIAM, Philadelphia, 1995, pp. 43-49.
    • (1995) Nonlinear Problems in Applied Mathematics , pp. 43-49
    • Auchmuty, G.1
  • 4
    • 0022054612 scopus 로고
    • A variational approach for the vector potential formulation of the Stokes and Navier-Stokes problems in three-dimensional domains
    • Bendali, A., Dominguez, J. M. and Gallic, S., 'A variational approach for the vector potential formulation of the Stokes and Navier-Stokes problems in three-dimensional domains', J. Math. Anal. Appl., 107, 537-560 (1985).
    • (1985) J. Math. Anal. Appl. , vol.107 , pp. 537-560
    • Bendali, A.1    Dominguez, J.M.2    Gallic, S.3
  • 7
    • 0001878229 scopus 로고
    • 2-theory of the Maxwell operator in arbitrary domains
    • 2-theory of the Maxwell operator in arbitrary domains', Russ. Math. Surv., 42, 75-96 (1987).
    • (1987) Russ. Math. Surv. , vol.42 , pp. 75-96
    • Birman, M.1    Solomyak, M.2
  • 8
    • 84972517043 scopus 로고
    • On the equations rot r = g and div u = f with zero boundary conditions
    • Borchers, W. and Sohr H., 'On the equations rot r = g and div u = f with zero boundary conditions', Hokkaido Math. J., 19, 67-87 (1990).
    • (1990) Hokkaido Math. J. , vol.19 , pp. 67-87
    • Borchers, W.1    Sohr, H.2
  • 9
    • 84988168833 scopus 로고
    • A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains
    • Costabel, M., 'A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains', Math. Meth. in the Appl. Sci., 12, 365-368 (1990).
    • (1990) Math. Meth. in the Appl. Sci. , vol.12 , pp. 365-368
    • Costabel, M.1
  • 10
    • 0003074690 scopus 로고
    • Elliptic Boundary Value Problems on Corner Domains
    • Springer, Berlin
    • Dauge, M., Elliptic Boundary Value Problems on Corner Domains, Lecture Notes in Mathematics, Vol. 1341, Springer, Berlin, 1988.
    • (1988) Lecture Notes in Mathematics , vol.1341
    • Dauge, M.1
  • 11
    • 0008276077 scopus 로고
    • Neumann and mixed problems on curvilinear polyhedra
    • Dauge, M., 'Neumann and mixed problems on curvilinear polyhedra', Integr. Equat. Oper. Theory, 15, 224-261 (1992).
    • (1992) Integr. Equat. Oper. Theory , vol.15 , pp. 224-261
    • Dauge, M.1
  • 13
    • 85034310487 scopus 로고
    • Internal Report 83015, Laboratoire d'Analyse Numérique de l'Université Pierre et Marie Curie
    • 3', Internal Report 83015, Laboratoire d'Analyse Numérique de l'Université Pierre et Marie Curie, 1983.
    • (1983) 3
    • Dominguez, J.M.1
  • 14
    • 0025503082 scopus 로고
    • Discrete vector potential representation of a divergence-free vector field in three-dimensional domains: Numerical analysis of a model problem
    • Dubois, F., 'Discrete vector potential representation of a divergence-free vector field in three-dimensional domains: Numerical analysis of a model problem', SIAM J. Numer. Anal., 27, 1103-1141 (1990).
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 1103-1141
    • Dubois, F.1
  • 16
    • 11744344326 scopus 로고
    • Vecteur de courant et fluides parfaits en aérodynamique numérique tridimensionnelle
    • El Dabaghi, F. and Pironneau, O. 'Vecteur de courant et fluides parfaits en aérodynamique numérique tridimensionnelle', Numer, Math., 48, 561-589 (1986).
    • (1986) Numer, Math. , vol.48 , pp. 561-589
    • El Dabaghi, F.1    Pironneau, O.2
  • 17
    • 0001953250 scopus 로고
    • Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcalion
    • Foias, C. and Temam, R. 'Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcalion'. Ann. Sc. Norm. Sup. Pisa, V, 29-63 (1978).
    • (1978) Ann. Sc. Norm. Sup. Pisa , vol.5 , pp. 29-63
    • Foias, C.1    Temam, R.2
  • 18
    • 84980081763 scopus 로고
    • Differential forms on Riemannian manifolds
    • Friedrichs, K. O. 'Differential forms on Riemannian manifolds', Comm. Pure Appl. Math., 8, 551-590 (1995).
    • (1995) Comm. Pure Appl. Math. , vol.8 , pp. 551-590
    • Friedrichs, K.O.1
  • 19
    • 0038077120 scopus 로고
    • 3
    • The Navier-Stokes Equations, Theory and Numerical Methods, Proc. Conf., Oberwolfach, 1988 (J. G. Heywood, K. Masuda, R. Rautmann and V. A. Solonnikov eds), Springer
    • 3', in: The Navier-Stokes Equations, Theory and Numerical Methods, Proc. Conf., Oberwolfach, 1988 (J. G. Heywood, K. Masuda, R. Rautmann and V. A. Solonnikov eds), Lecture Notes in Mathematics, Vol. 1431, Springer, 1990.
    • (1990) Lecture Notes in Mathematics , vol.1431
    • Girault, V.1
  • 20
    • 84988167309 scopus 로고
    • A stream function-vorticity for the exterior Stokes problem in weighted Sobolev spaces
    • Girault, V. Giroire, J and Sequeira, A. 'A stream function-vorticity for the exterior Stokes problem in weighted Sobolev spaces', Math. Meth. in the Appl. Sci., 15, 345-363 (1992)
    • (1992) Math. Meth. in the Appl. Sci. , vol.15 , pp. 345-363
    • Girault, V.1    Giroire, J.2    Sequeira, A.3
  • 22
    • 0002330152 scopus 로고
    • Sur une inégalité de coercivité
    • Gobert, J. 'Sur une inégalité de coercivité', J. Math. Anal. Appl., 36, 518-528 (1971).
    • (1971) J. Math. Anal. Appl. , vol.36 , pp. 518-528
    • Gobert, J.1
  • 25
    • 0004809471 scopus 로고
    • Compaaté par compensation II
    • E. De Giorgi E. Magenes and U. Mosco, eds, Pitagora Editrice, Bologne
    • Murat, F., 'Compaaté par compensation II', in: Proc. Int. Meeting on Recent Methods in Non-Linear Analysis (E. De Giorgi E. Magenes and U. Mosco, eds), Pitagora Editrice, Bologne, 1979, PP 245-256.
    • (1979) Proc. Int. Meeting on Recent Methods in Non-Linear Analysis , pp. 245-256
    • Murat, F.1
  • 27
    • 85034282321 scopus 로고
    • Internal Report 49, C. M. A. P., École Polytechnique
    • 3'. Internal Report 49, C. M. A. P., École Polytechnique, 1979.
    • (1979) 3
    • Nedelec, J.-C.1
  • 29
    • 0001469934 scopus 로고
    • Espaces d'interpolation et théorème de Soboleff
    • Peetre, J. 'Espaces d'interpolation et théorème de Soboleff, Ann. Inst. Fourier, 16, 279-317 (1966).
    • (1966) Ann. Inst. Fourier , vol.16 , pp. 279-317
    • Peetre, J.1
  • 30
    • 84974265418 scopus 로고
    • On the boundary value problems of electro- and magnetostatics
    • Picard, R. 'On the boundary value problems of electro- and magnetostatics', Proc. Roy. Soc. Edinb. Sect. A, 92, 165-174 (1982).
    • (1982) Proc. Roy. Soc. Edinb. Sect. A , vol.92 , pp. 165-174
    • Picard, R.1
  • 31
    • 0004593401 scopus 로고
    • On an inequality of Friedrichs
    • Saranen, J. 'On an inequality of Friedrichs', Math. Scand., 51, 310-322 (1982).
    • (1982) Math. Scand. , vol.51 , pp. 310-322
    • Saranen, J.1
  • 34
    • 0000087793 scopus 로고
    • Mixed finite element approximation of the vector potential
    • Verfürth, R., 'Mixed finite element approximation of the vector potential', Numer. Math., 50, 685-695 (1987).
    • (1987) Numer. Math. , vol.50 , pp. 685-695
    • Verfürth, R.1
  • 35
    • 84979103896 scopus 로고
    • A local compactness theorem for Maxwell's equations
    • Weber, C. 'A local compactness theorem for Maxwell's equations'. Math. Meth. in the Appl. Sci., 2, 12-25 (1980).
    • (1980) Math. Meth. in the Appl. Sci. , vol.2 , pp. 12-25
    • Weber, C.1


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