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On the coupling of boundary integral and finite element methods. (English) Zbl 0451.65083

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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[1] Philippe G. Ciarlet, The finite element method for elliptic problems, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. Studies in Mathematics and its Applications, Vol. 4. · Zbl 0383.65058
[2] M. DJAOUA, Equations Intégrales pour un Problème Singulier dans le Plan, These 3é cycle, Paris, 1977.
[3] J. GIROIRE, Rapport Interne à l’Ecole Polytechnique, Centre de Mathématiques Appliquées, Palaiseau, 1976.
[4] Donald Greenspan and Peter Werner, A numerical method for the exterior Dirichlet problem for the reduced wave equation, Arch. Rational Mech. Anal. 23 (1966), 288 – 316. · Zbl 0161.12701
[5] George C. Hsiao and Wolfgang L. Wendland, A finite element method for some integral equations of the first kind, J. Math. Anal. Appl. 58 (1977), no. 3, 449 – 481. · Zbl 0352.45016
[6] M. N. Le Roux, Méthode d’éléments finis pour la résolution numérique de problèmes extérieurs en dimension 2, RAIRO Anal. Numér. 11 (1977), no. 1, 27 – 60, 112 (French, with English summary). · Zbl 0382.65055
[7] J. C. NEDELEC, Cours de l’Ecole d’Eté d’Analyse Numérique, C.E.A., I.R.I.A., E.P.F., 1977.
[8] J.-C. Nédélec and J. Planchard, Une méthode variationnelle d’éléments finis pour la résolution numérique d’un problème extérieur dans \?³, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 7 (1973), no. R-3, 105 – 129 (French, with Loose English summary). · Zbl 0277.65074
[9] R. Seeley, Topics in pseudo-differential operators, Pseudo-Diff. Operators (C.I.M.E., Stresa, 1968) Edizioni Cremonese, Rome, 1969, pp. 167 – 305.
[10] P. Silvester and M.-S. Hsieh, Finite-element solution of 2-dimensional exterior-field problems, Proc. Inst. Elec. Engrs. 118 (1971), 1743 – 1748.
[11] O. C. Zienkiewicz, D. W. Kelly, and P. Bettess, The coupling of the finite element method and boundary solution procedures, Internat. J. Numer. Methods Engrg. 11 (1977), no. 2, 355 – 375. · Zbl 0347.65048
[12] W. L. Wendland, Elliptic systems in the plane, Monographs and Studies in Mathematics, vol. 3, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1979. · Zbl 0396.35001
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