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Giroire, J.; Nedelec, J. C.

Numerical solution of an exterior Neumann problem using a double layer potential. (English) Zbl 0405.65060

Math. Comput. 32, 973-990 (1978).
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Cited in 1 Review
Cited in 41 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65R20 Numerical methods for integral equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations

Keywords:

Numerical Solution; Exterior Neumann Problem; Double Layer Potential; Variational Formulation; Laplace Operator; Finite Element Method; Optimal Error Estimates
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\textit{J. Giroire} and \textit{J. C. Nedelec}, Math. Comput. 32, 973--990 (1978; Zbl 0405.65060)
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References:

[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] P. G. Ciarlet and P.-A. Raviart, General Lagrange and Hermite interpolation in \?\(^{n}\) with applications to finite element methods, Arch. Rational Mech. Anal. 46 (1972), 177 – 199. · Zbl 0243.41004
[3] M. DJAOUA, Méthode d’Éléments Finis pour la Résolution d’un problème extérieur dans \( {{\mathbf{R}}^3}\) , Rapport Interne du Centre de Mathématiques Appliquées de l’Ecole Polytechnique, no. 3, 1975.
[4] J. GIROIRE, Formulation Variationnelle par Équations Intégrales de Problèmes aux Limites Extérieurs, Rapport Interne du Centre de Mathématiques Appliquées de l’Ecole Polytechnique, no. 6, 1976.
[5] J. GIROIRE, Mise en Oeuvre Numérique de la Résolution par Potentiel de Double Couche du Probleme de Neumann Extérieur, Rapport Interne du Centre de Mathématiques Appliquées de l’Ecole Polytechnique. (To appear.)
[6] 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 (French). · Zbl 0247.35041
[7] 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
[8] Marie-Noëlle Le Roux, Équations intégrales pour le problème du potentiel électrique dans le plan, C. R. Acad. Sci. Paris Sér. A 278 (1974), 541 – 544 (French). · Zbl 0283.45006
[9] Jacques L. Lions, Problèmes aux limites dans les équations aux dérivées partielles, Deuxième édition. Séminaire de Mathématiques Supérieures, No. 1 (Été, vol. 1962, Les Presses de l’Université de Montréal, Montreal, Que., 1965 (French). · Zbl 0143.14003
[10] J. L. LIONS & E. MAGENES, Problèmes aux Limites Non Homogènes et Applications, Dunod, Paris, 1968. · Zbl 0165.10801
[11] J. N. Lyness, An error functional expansion for \?-dimensional quadrature with an integrand function singular at a point, Math. Comp. 30 (1976), no. 133, 1 – 23. · Zbl 0343.65007
[12] J. N. Lyness, Applications of extrapolation techniques to multidimensional quadrature of some integrand functions with a singularity, J. Computational Phys. 20 (1976), no. 3, 346 – 364. · Zbl 0336.65015
[13] S. G. Mikhlin, Mathematical physics, an advanced course, With appendices by V. M. Babič, V. G. Maz\(^{\prime}\)ja and I. Ja. Bakel\(^{\prime}\)man. Translated from the Russian. North-Holland Series in Applied Mathematics and Mechanics, Vol. 11, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1970. · Zbl 0202.36901
[14] J.-C. Nédélec, Curved finite element methods for the solution of singular integral equations on surfaces in \?³, Comput. Methods Appl. Mech. Engrg. 8 (1976), no. 1, 61 – 80. · Zbl 0333.45015
[15] 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
[16] P. P. ZABREYKO, et al., Integral Equations, A Reference Text, Noordhoff, Leyden, 1975.
[17] O. C. Zienkiewicz, The finite element method in engineering science, McGraw-Hill, London-New York-Düsseldorf, 1971. The second, expanded and revised, edition of The finite element method in structural and continuum mechanics. · Zbl 0237.73071
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