Prewavelet approximations for a system of boundary integral equations for plates with free edges on polygons

Mathematical Methods in the Applied Sciences

Volumn 21, Issue 13, 1998, Pages 1233-1267

  Bourgeois, Christian ^a   Nicaise, Serge ^a  

^a UNIVERSITÉ DE VALENCIENNES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; INTEGRAL EQUATIONS; NUMERICAL METHODS; PIECEWISE LINEAR TECHNIQUES; POLYNOMIALS; STIFFNESS MATRIX; VARIATIONAL TECHNIQUES;

BOUNDARY INTEGRAL EQUATIONS; GALERKIN METHOD; PREWAVELET APPROXIMATIONS;

APPROXIMATION THEORY;

EID: 0032166734     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1476(19980910)21:13<1233::AID-MMA994>3.0.CO;2-B     Document Type: Article

References (34)

1. Adams, R. A., Sobolev Spaces, Academic Press, New York, 1975.
2. Auscher, P., 'Ondeletters à support compact et conditions aux limites', J. Functional Anal., 111, 29-43 (1993).
3. Bacry, E., Mallat, S. and Papanicolaou, G., 'A wavelet based space-time adaptive numerical method for partial differential equations', RAIRO Modèl. Math. Anal. Numèr., 26, 793-834 (1992).
4. Blum, H. and Rannacher, R., 'On the boundary value problem of the biharmonic operator on domains with angular corners', Math. Meth. in the Appl. Sci., 2, 556-581 (1980).
5. Bourlard, M., 'Problèmes de Dirichlet pour le bilaplacien dans un polygone: résolution par éléments finis frontières raffinés', C. R. Acad. Sc. Paris, Sér 1, 306, 461-466 (1988).
6. Bourlard, M., 'Méthodes d'eléments finis de bord raffinés pour des problémes aux limites concernant le laplacien et le bilaplacien dans des domaines polygonaux du plan', Thesis, Université de Mons (Belgium), 1988.
7. Bourlard, M., and Nicaise, S., 'Abstract Green formula and applications to boundary integral equations', Num. Funct. Anal. Opt., 18, 667-689 (1997).
8. Buhmann, M. and Michelli, C. A., 'Spline prewalets for non-uniform konts', Numer. Math., 61, 455-474 (1992).
9. Chui, C. K. and Wang, J., 'Introduction to wavelets', Wavelet Analysis and Its Applications Vol. 1, Acadamic Press, New York, 1992.
10. Ciarlet, P. G. 'The finite element method for elliptic problems', St. Mathematics and its applications, Vol. 4, North-Holland, Amsterdam, 1978.
11. Costabel, M., 'Boundary integral operators on Lipschitz domains: Elementray results', SIAM J. Math. Anal., 19, 613-626 (1988).
12. Costabel, M. and Wendland, W., 'Strong ellipticity of boundary integral operators', J. Reine Angew. Math. 372, 39-63 (1986).
13. Dahmen, W., Prossdorf, S. and Schneider, R., 'Multiscale methods for pseudodifferential equations on Smooth manifolds', in: Proc. int. conf. on wavelets: Theroy, Algorithm and Applications, (C. K. Chui, L. Montefusco, L. Puccio eds.), pp. 385-424, Academic Press, New York, 1994.
14. Dahmen, W., Prossdorf, S. and Schneider, R., 'Wavelet approximation methods for pseudodifferential equations I: Stability and convergence', Math. Z., 215, 583-620 (1994).
15. Dahmen, W., Prossdorf, S. and Schneider, R., 'Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solution', Ad. Comput. Math., 1, 259-335 (1993).
16. Dahmen, W. and Kunoth, A., 'Multilevel preconditioning', Numer. Math., 63, 315-344 (1992).
17. Daubechies, I., 'Ten lectures on wavelets', CBMS Lecture Notes, Vol. 61, SIAM, Philadelphia, 1992.
18. Girorie, J. and Nédélec, J. C., 'A new system of boundary integral equations for plates with free edges', Math. Meth. Appl. Sci., 8, 755-772 (1995).
19. Goubet, O., 'Nonlinear Galerkin methods using hierarchical almost-orthogonal finite elements bases', Nonlinear Anal. T M P, 20, 223-247 (1993).
20. Grisvard, P. 'Elliptic problems in nonsmooth Domains', Monographs and Studies in Mathematics, Vol. 21, Pitman, Boston, 1985.
21. Jouini, A. and Lemarié-Rieusset, P. G., 'Analyse multi-résoultion bi-orthogonale sur l'intervalle et applications', Ann. Inst. Henri Poincaré Anal. non linéaire, 10, 453-476 (1933).
22. Lions, J.-L. and Magenes, E., Probléms Aux Limites Non-Homogénes et Applications, Vol. 1, Dunod, Paris, 1968.
23. Meyer, Y., 'Ondelettes et Opérateurs 2: Opérateur de Calderon-Zygmund', Hermann, Paris, 1990.
24. Meyer, Y., 'Ondelettes sur l'intervalle', Rev. Mat. Iberoamericana, 7, 115-133 (1992).
25. Nazaret, C., 'A system of boundary integral equations for polygonal plates with free edges', Math. Meth. Appl. Sci., 1997, to appear.
26. Nicaise, S., 'Polygonal interface problems', Series Methoden und Verfahren der Mathematischen Physik Vol. 39, Peter Lang Verlag, 1993.
27. Nédélec, J.-C., Approximation des Équations Intégrales en Mécanique et en Physique, Ecole polytechnique, Palaiseau, 1977.
28. Oswald, P., 'On function spaces related to finite element approximation theory', Z. Anal. Anwendungen, 9, 1990, 43-64.
29. Oswald, P., 'Hierarchical conforming finite element methods for the biharmonic equation', SIAM J. Numer. Anal., 29, 1610-1625 (1992).
30. Oswald, P., 'Multilevel Finite Element Approximation: Theory and Applications'. Teubner, Stuttgart, 1994.
31. Petersdorff, T. v. and Schwab, C., 'Wavelet approximations for first kind boundary integral equations on polygons', Numer. Math., 74, 479-519 (1996).
32. Peterdorff, T. v. and Stephan, E. P., 'A multigrid method on graded meshes for a hypersingular integral equation', Preprint. University of Maryland, 1996.
33. Schumaker, L., Spline Functions: Basic Theory, Wiley, New York, 1981.
34. Triebel, H., Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, New York, Oxford, 1978.