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On the \(h\)-\(p\) version of the boundary element method for Symm’s integral equation on polygons. (English) Zbl 0842.65076

Summary: We present the numerical implementation of, and numerical experiments for, the Galerkin approximation of Symm’s integral equation using the \(h\), \(p\), and \(h\)-\(p\) methods. Numerical results obtained using an adaptive algorithm are also given. The theoretical results for these methods are summarized and are compared with the experimental results.

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
65R20 Numerical methods for integral equations
35J25 Boundary value problems for second-order elliptic equations
35C15 Integral representations of solutions to PDEs
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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References:

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