Error estimates for discretized Galerkin and collocation boundary element methods for time harmonic Dirichlet screen problems in ℝ³

 Access to full text

 Full (PDF)

1. [1] D. Colton and R. Kress, Integral Equation Methods in Scattering Theory, Wiley, 1983. Zbl0522.35001
2. [2] M. Costabel, Boundary integral operators on Lipschitz domains: Elementary results, SIAM J. Math. Anal. 19 (1988), 613-626. Zbl0644.35037
3. [3] M. Costabel and W. McLean, Spline collocation for strongly elliptic equations on the torus, Numer. Math. 62 (1992), 511-538. Zbl0767.65079
4. [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. Zbl0765.65108
5. [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. Zbl0803.65107
6. [6] M. Costabel and E. Stephan, Duality estimates for the numerical solution of integral equations, Numer. Math. 54 (1988), 339-353. Zbl0663.65141
7. [7] M. Dauge, Elliptic Boundary Value Problems in Corner Domains - Smoothness and Asymptotics of Solutions, Lecture Notes in Math. 1341, Springer, Berlin 1988. 
8. [8] P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York 1975. Zbl0304.65016
9. [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. Zbl0493.65011
10. [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. 
11. [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. Zbl0731.65119
12. [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. 
13. [13] T. Ha Duong, On the transient acoustic scattering by a flat object, Japan J. Appl. Math. 7 (3) (1990), 489-513. Zbl0719.35063
14. [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. Zbl0419.65088
15. [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. Zbl0352.45016
16. [16] R. C. MacCamy and E. Stephan, Solution procedures for three-dimensional eddy current problems, ibid. 101 (1984), 348-379. Zbl0563.35054
17. [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. Zbl0277.65074
18. [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. Zbl0756.65130
19. [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. 
20. [20] T. v. Petersdorff, Randwertprobleme der Elastizitätstheorie für Polyeder-Singularitäten und Approximation mit Randelementmethoden, Dissertation, Darmstadt 1989. Zbl0709.73009
21. [21] S. Prössdorf, Numerische Behandlung singulärer Integralgleichungen, Z. Angew. Math. Mech. 69 (1989), T5-T13. 
22. [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. Zbl0686.65096
23. [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. Zbl0737.47043
24. [24] S. Prössdorf and R. Schneider, Spline approximation methods for multidimensional periodic pseudodifferential equations, Integral Equations Operator Theory 15 (1992), 626-672. Zbl0757.65146
25. [25] A. Rathsfeld, On the stability of quadrature methods for the double layer potential equation over the boundary of the polyhedron, manuscript, May 1991. 
26. [26] G. Schmidt, Splines und die näherungsweise Lösung von Pseudodifferentialgleichungen auf geschlossenen Kurven, report R-MATH-09/86, Karl-Weierstrass-Institut, Berlin 1986. 
27. [27] R. Schneider, Stability of a spline collocation method for strongly elliptic multidimensional singular integral equations, Numer. Math. 58 (1991), 855-873. Zbl0724.65134
28. [28] C. Schwab and W. L. Wendland, On numerical cubatures of singular surface integrals in boundary element methods, ibid. 62 (1992), 343-369. Zbl0761.65012
29. [29] E. Stephan, Boundary integral equations for screen problems in ℝ³, Integral Equations Operator Theory 10 (1987), 236-257. Zbl0653.35016
30. [30] A. H. Strout and D. Secrest, Gaussian Quadrature Formulas, Prentice-Hall, 1966. Zbl0156.17002
31. [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. 
32. [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.