The superconvergence of a Galerkin collocation method for first kind boundary integral equations on smooth curves

Journal of Computational and Applied Mathematics

Volumn 72, Issue 1, 1996, Pages 1-20

  Shu, H Z ^a,b  

^a UNIVERSITÉ DE RENNES 1   (France)

^b SOUTHEAST UNIVERSITY   (China)

Author keywords

Boundary integral equations; Galerkin collocation method; Superconvergence

Indexed keywords

BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; INTEGRAL EQUATIONS; NUMERICAL ANALYSIS; PIECEWISE LINEAR TECHNIQUES; PROBLEM SOLVING;

BOUNDARY INTEGRAL EQUATIONS; GALERKIN COLLOCATION METHOD; LOGARITHMIC KERNEL; SMOOTH CURVES; SUPERCONVERGENCE;

FINITE ELEMENT METHOD;

EID: 0030194057     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/0377-0427(95)00242-1     Document Type: Article

References (15)

1. K.E. Atkinson and G.A. Chandler, Boundary integral equation methods for solving Laplace's equation with nonlinear boundary conditions: the smooth boundary case. Math. Comput. 55 (1990) 451-472.
2. C.A. Brebbia, J.C.F. Telles and L.C. Wrobel, Boundary Element Techniques: Theory and Applications in Engineering (Springer, Berlin, 1984).
3. J. Giroire, Integral equation methods for exterior problems for the Helmholtz equation, Rapport interne no40 du centre de Mathématiques Appliquées de l'école Polytechnique, Palaiseau, 1978.
4. J. Giroire, Mise en oeuvre de méthodes d'éléments finis de frontière, Cours du D.E.A. d'Analyse Numérique, Université Pierre et Marie Curie, Année 1987-1988.
5. F. Hartmann, Introduction to Boundary Elements: Theory and Application (Springer, Berlin, 1989).
6. 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.
7. G.C. Hsiao, P. Kopp and W.L. Wendland. Some applications of a Galerkin-collocation method for boundary integral equations of the first kind. Math. Meth. Appl. Sci. 6 (1984) 280-325.
8. ème cycle. Université de Rennes I, France, 1974.
9. J.C. Nédélec, Approximation des équations intégrales en mécanique et en physique. Rapport Centre de Mathématiques Appliquées, Ecole Polytechnique, 1977.
10. J.C. Nédélec, Analyse mathématique et calcul numérique pour les sciences et les techniques, in: R. Dautray and J.L. Lions, Eds., Méthodes intégrales et numériques, Vol. 6 (Masson, Paris, 1988).
11. I.H. Sloan, Error analysis of boundary integral methods, Acta Numerica 1 (1992) 1-53.
12. I.H. Sloan and A. Spence, The Galerkin method for integral equations of the first kind with logarithmic kernel: Theory, I M A J. Numer. Anal. 8 (1988) 105-122.
13. I.H. Sloan and A. Spence, The Galerkin method for the integral equations of the first kind with logarithmic kernel: applications, I M A J. Numer. Anal. 8 (1988) 123-140.
14. W.L. Wendland, Boundary element methods for elliptic problems, in: H. Schatz, V. Thomée and W.L. Wendland, Eds., Mathematical Theory of Finite and Boundary Element Methods (Birkhäuser, Basel, 1990) 219-276.
15. Y. Yan and I.H. Sloan, On integral equations of the first kind with logarithmic kernel, J. Int. Equations Appl. 1 (1988) 517-548.