Pointwise convergence of some boundary element methods. Part II
ESAIM: Modélisation mathématique et analyse numérique, Tome 22 (1988) no. 2, pp. 343-362. 
@article{M2AN_1988__22_2_343_0,
     author = {Rannacher, Rolf and Wendland, Wolfgang L.},
     title = {Pointwise convergence of some boundary element methods. {Part} {II}},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {343--362},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {22},
     number = {2},
     year = {1988},
     mrnumber = {945128},
     zbl = {0648.65092},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1988__22_2_343_0/}
}
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Rannacher, Rolf; Wendland, Wolfgang L. Pointwise convergence of some boundary element methods. Part II. ESAIM: Modélisation mathématique et analyse numérique, Tome 22 (1988) no. 2, pp. 343-362. http://www.numdam.org/item/M2AN_1988__22_2_343_0/

[1] M. S. Bou El Seoud, Kollokationsmethode für schwach singuläre Inté-gralgleichungen erster Art. Z. Angew. Math. Mech. 59, T45-T47 (1979). | Zbl

[2] M. S. Agranovich, Spectral properties of diffraction problems. In : The General Method of Natural Vibrations in Diffraction Theory. (Russian)(N. N. Voitovic, K. Z. Katzenellenbaum and A. N. Sivov) Izdat. Nauka, Mos-cow 1977. | MR

[3] M. A. Aleksidze, The Solution of Boundary Value Problems with the Method of Expansion with Respect to Nonorthonormal Functions. Nauka, Moscow 1978 (Russian). | MR

[4] D. N. Arnold and W. L. Wendland, On the asymptotic convergence of collocation methods. Math. Comp. 41, 349-381 (1983). | MR | Zbl

[5] D. N. Arnold and W. L. Wendland, The convergence of spline collocationfor strongly elliptic equations on curves. Numer. Math. 47, 317-341 (1985). | MR | Zbl

[6] I. Babuska and A. K. Ziz, Survey lectures on the mathematical foundations of finite element method. In The Mathematical Foundations o f the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, ed.), pp. 3-359, Academic Press, New York 1972. | MR | Zbl

[7] M. Costabel and E. Stephan, The normal derivative of the double layer potential on polygons and Galerkin approximation. Applicable Anal. 16, 205-288 (1983). | MR | Zbl

[8] Costabel and E. Stephan, A direct boundary integral equation method for transmission problems. J. Appl. Anal. Appl. 106, 367-413 (1985). | MR | Zbl

[9] M. Costabel and W. L. Wendland, Strong ellipticity of boundary integral operators. J. Reine Angew. Math. 372, 34-63 (1986). | MR | Zbl

[10] P. Filippi, Layer potentials and acoustic diffraction. J. Sound and Vibration 54, 473-500 (1977). | Zbl

[11] J. Frehse and R. Rannacher, Eine L'-Fehlerabschätzung für diskrete Grundlösungen in der Mehtode der finiten Elemente. In : Finite Elemente, Tagungsband Bonn. Math. Schr. 89, 92-114 (1976). | MR | Zbl

[12] J. Giroire and J. C. Nedelec, Numerical solution of an exterior Neumann problem using a double layer potential. Math. Comp. 32, 973-990 (1978). | MR | Zbl

[13] T. Ha Duong, A finite element method for the double layer potential solutions of the Neumann exterior problem. Math. Meth. Appl. Sci. 2, 191-208 (1980). | MR | Zbl

[14] F. K. Hebeker, An integral equation of the first kind for a free boundary value problem of the stationary Stokes equations. Math. Meth. Appl. Sci. 9, 550-575 (1987). | MR | Zbl

[15] L. Hormander, Pseudo-differential operators and non-elliptic boundary problems. Annals Math. 83, 129-209 (1966). | MR | Zbl

[16] H. P. Hoidin, Die Kollokationsmethode angewandt auf die Symmsche Integralgleichung. Doctoral Thesis, EHT Zürich, Switzerland 1983. | Zbl

[17] G. C. Hsia and W. L. Wendland, A finite element method for some integral equations of the first kind. J. Math. Anal. Appl. 58, 449-481 (1977). | MR | Zbl

[18] G. C. Hsiao and W. L. Wendland, The Aubin-Nitsche lemma for integral equations. Journal of Integral Equations 3, 299-315 (1981). | MR | Zbl

[19] F. Natterer, Über die punktweise Konvergenz finiter Elemente. Number. Math. 25, 67-77 (1975). | MR | Zbl

[20] J. C. Nedelec, Approximation des équations intégrales en mécanique et en physique. Lecture Notes, Centre de Math. Appl. Ecole Polytechnique, 91128 Palaiseau, France, 1977.

[21] J. C. Nedelec, Approximation par potentiel de double couche du problème de Neumann extérieur. C. R. Acad. Sci. Paris, Ser. A 286, 616-619 (1978). | MR | Zbl

[22] J. C. Nedelec, Integral equations with non integrable kernels. Integral Equations Operator Theory 5, 562-572 (1982). | MR | Zbl

[23] J. A. Nitsche, L ∞ -convergence of finite element approximation. Second Conference on Finite Elements, Rennes, France, 1975. | MR | Zbl

[24] P. M. Prenter, Splines and Variational Methods. John Wiley & Sons, New York 1975. | MR | Zbl

[25] S. Prössdorf and G. Schmidt, A finite elementcollocation method for singular integral equations. Math. Nachr, 100, 33-60 (1981). | MR | Zbl

[26] R. Rannacher, Punktweise Konvergenz der Methode der finiten Elemente beim Plattenproblem. Manuscripta Math. 19, 401-416 (1976). | MR | Zbl

[27] R. Rannacher, On non conforming and mixed finite element methods for plate bending problems. The linear case. R.A.I.R.O. Anal. Numér. 13, 369-387 (1979). | Numdam | MR | Zbl

[28] R. Rannacher and R. Scott, Some optimal error estimates for piecewise linear finite element approximations. Math. Comp. 38, 437-445 (1982). | MR | Zbl

[29] R. Rannacher and W. L. Wendland, On the order of pointwise convergence of some boundary element methods. Part I. Operators of negative and zero order. Math. Modelling and Numer. Analysis 19, 65-88 (1985). | Numdam | MR | Zbl

[30] A. H. Schatz and L. B. Wahlbin, Maximum norm error estimates in the finite element method for Poisson's equation on plante domains with corner. Math. Comp. 32, 73-109 (1978). | MR | Zbl

[31] G. Schmidt, The convergence of Galerkin and collocation methods with splines for pseudodifferential equations on closed curves. Z. Anal. Anwendungen 3, 371-384 (1984). | MR | Zbl

[32] R. Scott, Optimal L ∞ -estimatees for the finite element method on irregular meshes. Math. Comp. 30, 681-697 (1976). | MR | Zbl

[33] E. Stephan and W. L. Wendland, Remarks to Galerkin and least squares methods with finite elements for general elliptic problems. Manuscripta Geodaetica 1, 93-123 (1976) and Springer Lecture Notes in Math. 564, 461-471 (1976). | MR | Zbl

[34] G. Strang, Approximation in the finite element method. Num. Math. 19 (1972). | MR | Zbl

[35] M. E. Taylor, Pseudodifferential Operators. Princeton University Press,Princeton, New Jersey 1981. | MR | Zbl

[36] F. Treves, Pseudodifferential Operators. Plenum Press, New York, London 1980. | MR

[37] J. O. Watson, Advanced implementation of the boundary element method fortwo- and three-dimensional elastostatics. In : Developments in Boundary Element Methods. I. Banerjee and R. Butterfield (eds.), Appl. Sciences Publ. LTD, London, 31-63 (1979). | Zbl

[38] W. L. Wendland, Boundary element methods and their asymptotic conver-gence. . In : Theoretical Acoustics and Numerical techniques. P. Filippi (éd.), CISM Courses and Lectures No.277, Springer-Verlag, Wien, New York, 135-216 (1983). | MR | Zbl