Error estimates for discretized Galerkin and collocation boundary element methods for time harmonic Dirichlet screen problems in ℝ³
Penzel, F.
Banach Center Publications, Tome 29 (1994), p. 115-134 / Harvested from The Polish Digital Mathematics Library
Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:262593
@article{bwmeta1.element.bwnjournal-article-bcpv29z1p115bwm,
     author = {Penzel, F.},
     title = {Error estimates for discretized Galerkin and collocation boundary element methods for time harmonic Dirichlet screen problems in $\mathbb{R}$$^3$},
     journal = {Banach Center Publications},
     volume = {29},
     year = {1994},
     pages = {115-134},
     zbl = {0842.65073},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv29z1p115bwm}
}
Penzel, F. Error estimates for discretized Galerkin and collocation boundary element methods for time harmonic Dirichlet screen problems in ℝ³. Banach Center Publications, Tome 29 (1994) pp. 115-134. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv29z1p115bwm/

[000] [1] D. Colton and R. Kress, Integral Equation Methods in Scattering Theory, Wiley, 1983. | Zbl 0522.35001

[001] [2] M. Costabel, Boundary integral operators on Lipschitz domains: Elementary results, SIAM J. Math. Anal. 19 (1988), 613-626. | Zbl 0644.35037

[002] [3] M. Costabel and W. McLean, Spline collocation for strongly elliptic equations on the torus, Numer. Math. 62 (1992), 511-538. | Zbl 0767.65079

[003] [4] M. Costabel, F. Penzel and R. Schneider, Error analysis of a boundary element collocation method for a screen problem in ℝ³, Math. Comp. 58 (198) (1992), 575-586. | Zbl 0765.65108

[004] [5] M. Costabel, F. Penzel and R. Schneider, Convergence of boundary element collocation methods for Dirichlet and Neumann screen problems in ℝ³, Appl. Anal. 49 (1993), 101-117. | Zbl 0803.65107

[005] [6] M. Costabel and E. Stephan, Duality estimates for the numerical solution of integral equations, Numer. Math. 54 (1988), 339-353. | Zbl 0663.65141

[006] [7] M. Dauge, Elliptic Boundary Value Problems in Corner Domains - Smoothness and Asymptotics of Solutions, Lecture Notes in Math. 1341, Springer, Berlin 1988.

[007] [8] P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York 1975. | Zbl 0304.65016

[008] [9] M. G. Duffy, Quadrature over a pyramid or cube of integrands with a singularity at a vertex, SIAM J. Numer. Anal. 19 (6) (1982), 1260-1262. | Zbl 0493.65011

[009] [10] V. J. Ervin and E. P. Stephan, Experimental convergence of boundary element methods for the capacity of the electrified plate, Boundary Elem. 9 (1987), 167-175.

[010] [11] V. J. Ervin and E. P. Stephan, A boundary-element method with mesh refinement for a weakly singular integral equation, Comm. Appl. Numer. Methods 7 (4) (1991), 273-280. | Zbl 0731.65119

[011] [12] V. J. Ervin, E. P. Stephan and S. Abou el-Seoud, An improved boundary element method for the charge density of a thin electrified plate in ℝ³, Math. Methods Appl. Sci. 13 (1990), 291-303.

[012] [13] T. Ha Duong, On the transient acoustic scattering by a flat object, Japan J. Appl. Math. 7 (3) (1990), 489-513. | Zbl 0719.35063

[013] [14] G. C. Hsiao, P. Kopp and W. L. Wendland, A Galerkin collocation method for some integral equations of the first kind, Computing 25 (1980), 89-130. | Zbl 0419.65088

[014] [15] G. C. Hsiao and W. L. Wendland, A finite element method for some integral equations of the first kind, J. Math. Anal. Appl. 58 (1977), 449-481. | Zbl 0352.45016

[015] [16] R. C. MacCamy and E. Stephan, Solution procedures for three-dimensional eddy current problems, ibid. 101 (1984), 348-379. | Zbl 0563.35054

[016] [17] J. C. Nedelec and J. Planchard, Une méthode variationnelle d'éléments finis pour la résolution numérique d'un problème extérieur dans ℝ³, RAIRO 7 (1973), 105-129. | Zbl 0277.65074

[017] [18] F. Penzel, Error estimates for a discretized Galerkin method for a boundary integral equation in two dimensions, Numer. Methods Partial Differential Equations 8 (1992), 405-421. | Zbl 0756.65130

[018] [19] F. Penzel, Error estimates for discretized Galerkin and collocation boundary element methods for time harmonic Dirichlet screen problems in ℝ³, THD-Preprint, Technische Hochschule Darmstadt, 1991.

[019] [20] T. v. Petersdorff, Randwertprobleme der Elastizitätstheorie für Polyeder-Singularitäten und Approximation mit Randelementmethoden, Dissertation, Darmstadt 1989. | Zbl 0709.73009

[020] [21] S. Prössdorf, Numerische Behandlung singulärer Integralgleichungen, Z. Angew. Math. Mech. 69 (1989), T5-T13.

[021] [22] S. Prössdorf and A. Rathsfeld, Quadrature and Collocation methods for singular integral equations on curves with corners, Z. Anal. Anwendungen 8 (1989), 197-220. | Zbl 0686.65096

[022] [23] S. Prössdorf and R. Schneider, A spline collocation method for multidimensional strongly elliptic pseudodifferential operators of order zero, Integral Equations Operator Theory 14 (1991), 399-435. | Zbl 0737.47043

[023] [24] S. Prössdorf and R. Schneider, Spline approximation methods for multidimensional periodic pseudodifferential equations, Integral Equations Operator Theory 15 (1992), 626-672. | Zbl 0757.65146

[024] [25] A. Rathsfeld, On the stability of quadrature methods for the double layer potential equation over the boundary of the polyhedron, manuscript, May 1991.

[025] [26] G. Schmidt, Splines und die näherungsweise Lösung von Pseudodifferentialgleichungen auf geschlossenen Kurven, report R-MATH-09/86, Karl-Weierstrass-Institut, Berlin 1986.

[026] [27] R. Schneider, Stability of a spline collocation method for strongly elliptic multidimensional singular integral equations, Numer. Math. 58 (1991), 855-873. | Zbl 0724.65134

[027] [28] C. Schwab and W. L. Wendland, On numerical cubatures of singular surface integrals in boundary element methods, ibid. 62 (1992), 343-369. | Zbl 0761.65012

[028] [29] E. Stephan, Boundary integral equations for screen problems in ℝ³, Integral Equations Operator Theory 10 (1987), 236-257. | Zbl 0653.35016

[029] [30] A. H. Strout and D. Secrest, Gaussian Quadrature Formulas, Prentice-Hall, 1966. | Zbl 0156.17002

[030] [31] W. L. Wendland, Boundary element methods and their asymptotic convergence, in: Lecture Notes of the CISM Summer School on 'Theoretical Acoustics and Numerical Technique', Internat. Centre for Mechanical Sciences, Udine, Italy, 1983, P. Filippi (ed.), Lecture Notes in Phys., Springer, 135-216.

[031] [32] W. L. Wendland, Strongly elliptic boundary integral equations, in: The State of the Art in Numerical Analysis, A. Iserles and M. J. D. Powell (eds.), Clarendon Press, Oxford 1987, 511-562.