Kress, Rainer A Nyström method for boundary integral equations in domains with corners. (English) Zbl 0707.65078 Numer. Math. 58, No. 2, 145-161 (1990). The core of this work is a high order quadrature formula for integrals with endpoint singularities. The author obtains such a formula using the trapezoidal rule for the transformed integral. This quadrature rule is then applied in the Nyström method for a class of integral equations of the second kind with endpoint singularities. Finally, the method is applied to the boundary integral equations of the plane potential theory in domains with corners. Reviewer: C.I.Gheorghiu Cited in 4 ReviewsCited in 90 Documents MSC: 65N38 Boundary element methods for boundary value problems involving PDEs 65R20 Numerical methods for integral equations 65D32 Numerical quadrature and cubature formulas 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 31A25 Boundary value and inverse problems for harmonic functions in two dimensions Keywords:Dirichlet problem; Laplace equation; boundary element method; quadrature formula; integrals with endpoint singularities; Nyström method; boundary integral equations; domains with corners PDFBibTeX XMLCite \textit{R. Kress}, Numer. Math. 58, No. 2, 145--161 (1990; Zbl 0707.65078) Full Text: DOI EuDML References: [1] Atkinson, K.E., Graham, I.G.: An iterative variant of the Nystr?m method for boundary integral equations on nonsmooth boundaries. In: Whitemann, J.R. (ed.) The Mathematics of Finite Elements and Applications VI (MAFELAP 1987), pp 197-304. London: Academic Press 1988 [2] Costabel, M., Stephan, E.P.: Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation, Mathematical models and methods in mechanics, Banach Center Publications 15, Warsaw 1985, pp 175-251. · Zbl 0655.65129 [3] Costabel, M., Stephan, E.P.: On the convergence of collocation methods for boundary integral equations on polygons. Math. Comput.49, 467-478 (1987) · Zbl 0636.65122 [4] Cryer, C.W.: Numerical functional analysis. Clarendon Press: Oxford 1982 · Zbl 0494.65029 [5] Davis, P.J., Rabinowitz, P.: Methods of numerical integration. Academic Press: New York 1975 · Zbl 0304.65016 [6] Graham, I.G., Chandler, G.A.: High-order methods for linear functionals of solutions of second kind integral equations. SIAM J. Numer. Anal.25, 1118-1173 (1988) · Zbl 0661.65137 · doi:10.1137/0725064 [7] Grisvard, P.: Elliptic problems in nonsmooth domains. Boston: Pitman 1985 · Zbl 0695.35060 [8] Kress, R.: Linear integral equations. New York Berlin Heidelberg: Springer 1989 · Zbl 0671.45001 [9] Kress, R.: Boundary integral equations in time-harmonic acoustic scattering. Comput Math. Appl. (to appear) · Zbl 0731.76077 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.