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Curved finite element methods for the solution of singular integral equations on surfaces in \(R^3\). (English) Zbl 0333.45015


MSC:

45L05 Theoretical approximation of solutions to integral equations
65R20 Numerical methods for integral equations
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
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[1] Nedelec, J. C.; Planchard, J., Une méthode variationnelle d’éléments finis pour la résolution numérique d’un problème extérieur dans \(R^3\), R.A.I.R.O., 7, 105-129 (1973), R3 · Zbl 0277.65074
[2] Lions, J. L.; Magenes, E., Problèmes aux limites non homogènes (1968), Dunod: Dunod Paris · Zbl 0165.10801
[3] Ciarlet, P. G.; Raviart, P. A., General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods, Arch. Rat. Mech. Anal., 46, 177-199 (1972) · Zbl 0243.41004
[4] Stroud, A. H., Approximate calculation of multiple integrals (1972), Prentice Hall · Zbl 0379.65013
[5] Butzer, P. L.; Berens, H., Semi-groups of operators and approximations (1967), Springer: Springer Berlin · Zbl 0164.43702
[6] Seeley, R., Cours C.I.M.E., Stresa, 1968 (1969), Cremonese: Cremonese Rome
[7] Leroux, M. N., Equations intégrales pour le problème du potentiel électrique dans le plan, C.R.A.S., Paris (sér. math. A), 278, 541-544 (1974) · Zbl 0283.45006
[8] Leroux, M. N., Résolution numérique du problème du potentiel dans le plan par une méthode variationnelle d’éléments finis, Thèse de 3ème Cycle, Univ. Rennes (1974)
[9] Djaoua, M., Méthode d’éléments finis pour la résolution d’un problème extérieur dans \(R^3\), Rapport interne du Centre de Mathématiques Appliquées de l’Ecole Polytechnique, No 3 (1975)
[10] Rizzo, J. F., An integral equation approach to boundary value problems of classical elasto-plastics, Quarterly of Applied Mathematics, 25, 83 (1967) · Zbl 0158.43406
[11] Cruse, T. A., Application of the boundary integral equation method to three-dimensional stress analysis, Comp. Struct., 3, 309 (1973)
[12] Lachat, J. L., Application de la méthode des éléments finis à l’élasticité plane et aux corps de révolution, (Mémoires Techniques C.E.T.I.M., no. 9 (Sept. 1971))
[13] Hess, J. L.; Smith, A. M.O, Calculation of nonlifting potential flow about arbitrary three-dimensional bodies, J. Ship Res., 8, 22-44 (1964)
[14] Hess, J. L., Review of integral equation techniques for solving potential flow problems with emphasis on the surface source method, Comp. Meths. Appl. Mech. Eng., 5, 145-196 (1975) · Zbl 0299.76011
[15] Hess, J. L., Improved solution for potential flow about arbitrary axisymmetric bodies by the use of a higher-order surface source method, Comp. Meths. Appl. Mech. Eng., 5, 297-308 (1975) · Zbl 0298.76008
[16] G.C. Hsiao and W. Wendland, A finite element method for some integral equations of the first kind, to appear in J.M.A.A.; G.C. Hsiao and W. Wendland, A finite element method for some integral equations of the first kind, to appear in J.M.A.A. · Zbl 0352.45016
[17] Argyris, J. H., Energy theorems and structural analysis (1971), Butterworth: Butterworth London
[18] Ciarlet, P. G.; Raviart, P. A., Interpolation theory over curved elements with applications to finite element methods, Comp. Meths. Appl. Mech. Eng., 1, 217-249 (1972) · Zbl 0261.65079
[19] Ciarlet, P. G., La méthode des éléments finis appliquée aux coques, (LABORIA, Rapport de Recherche no. 113 (1975))
[20] Dubois, M.; Lachat, J. C., The integral formulation of boundary value problems, (Variational methods in engineering (1972), Univ. Southampton), 989 · Zbl 0317.73015
[21] Hanouzet, B., Espace de Sobolev avec poids. Application au problème de Dirichlet dans un demi-espace, Rend. Semin. Math. Univ. Padova, 46, 247-272 (1971) · Zbl 0247.35041
[22] Hormander, Linear partial differential operators (1963), Springer: Springer Berlin · Zbl 0108.09301
[23] Kupradze, V. D., Potential methods in the theory of elasticity (1965), Darvey · Zbl 0188.56901
[24] Lelong, J.; Ferrand, M., Géométrie différentielle (1963), Masson: Masson Paris · Zbl 0111.34302
[25] Mikhlin, S. G., Linear integral equations (1960), Gordon and Breach: Gordon and Breach New York · Zbl 0142.39201
[26] Zienkiewicz, O. C., The finite element method in engineering science (1971), McGraw-Hill: McGraw-Hill London · Zbl 0237.73071
[27] Lachat, J. L.; Watson, J. O., A second generation boundary integral equation program of the three-dimensional elastic analysis, C.E.T.I.M. (1974)
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