Summary
We give a convergence and error analysis for a Nyström method on a graded mesh for the numerical solution of boundary integral equations for the harmonic Dirichlet problem in plane domains with corners.
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Atkinson, K.E., Graham, I.G.: An iterative variant of the Nyström 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
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.
Costabel, M., Stephan, E.P.: On the convergence of collocation methods for boundary integral equations on polygons. Math. Comput.49, 467–478 (1987)
Cryer, C.W.: Numerical functional analysis. Clarendon Press: Oxford 1982
Davis, P.J., Rabinowitz, P.: Methods of numerical integration. Academic Press: New York 1975
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)
Grisvard, P.: Elliptic problems in nonsmooth domains. Boston: Pitman 1985
Kress, R.: Linear integral equations. New York Berlin Heidelberg: Springer 1989
Kress, R.: Boundary integral equations in time-harmonic acoustic scattering. Comput Math. Appl. (to appear)
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Dedicated to Professor L. Collatz on the occassion of his 80th birthday
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Kress, R. A Nyström method for boundary integral equations in domains with corners. Numer. Math. 58, 145–161 (1990). https://doi.org/10.1007/BF01385616
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DOI: https://doi.org/10.1007/BF01385616