The authors consider the interior Dirichlet problem for Laplace’s equation on planar domains with corners. They provide a complete analysis of a natural method of Nyström type based on the global Gauss–Lobatto quadrature rule, in order to approximate the solution of the corresponding double layer boundary integral equation. Mellin-type integral operators are involved and, as usual, a modification of the method close to the corners is needed. A new modification is proposed and the convergence and stability of the “modified” quadrature method are proved. Some numerical tests are also included.
A Nyström method for the numerical solution of a boundary integral equation related to the Dirichlet problem on domains with corners
LAURITA, Concetta
2015-01-01
Abstract
The authors consider the interior Dirichlet problem for Laplace’s equation on planar domains with corners. They provide a complete analysis of a natural method of Nyström type based on the global Gauss–Lobatto quadrature rule, in order to approximate the solution of the corresponding double layer boundary integral equation. Mellin-type integral operators are involved and, as usual, a modification of the method close to the corners is needed. A new modification is proposed and the convergence and stability of the “modified” quadrature method are proved. Some numerical tests are also included.File in questo prodotto:
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