Galerkin's method for boundary integral equations on polygonal domains
- 1 July 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
- Vol. 26 (1) , 1-13
- https://doi.org/10.1017/s033427000000429x
Abstract
A harmonic function in the interior of a polygon is the double layer potential of a distribution satisfying a second kind integral equation. This may be solved numerically by Galerkin's method using piecewise polynomials as basis functions. But the corners produce singularities in the distribution and the kernel of the integral equation; and these reduce the order of convergence. This is offset by grading the mesh, and the orders of convergence and superconvergence are restored to those for a smooth boundary.Keywords
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