A spectral Galerkin method for a boundary integral equation

Author:
W. McLean

Journal:
Math. Comp. **47** (1986), 597-607

MSC:
Primary 65R20; Secondary 45L10

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856705-2

MathSciNet review:
856705

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Abstract: We consider the boundary integral equation which arises when the Dirichlet problem in two dimensions is solved using a single-layer potential. A spectral Galerkin method is analyzed, suitable for the case of a smooth domain and smooth boundary data. The use of trigonometric polynomials rather than splines leads to fast convergence in Sobolev spaces of every order. As a result, there is rapid convergence of the approximate solution to the Dirichlet problem and all its derivatives uniformly up to the boundary.

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DOI:
https://doi.org/10.1090/S0025-5718-1986-0856705-2

Article copyright:
© Copyright 1986
American Mathematical Society