Postell, F. V.; Stephan, E. P. On the h-, p- and h-p versions of the boundary element method. - Numerical results. (English) Zbl 0732.65101 Comput. Methods Appl. Mech. Eng. 83, No. 1, 69-89 (1990). The authors present numerical results on two types of boundary integral equations of the first kind. The first one is Symm’s integral equation with logarithmic kernel and the second one is a hypersingular integral equation with the normal derivative of the double layer potential as kernel. They compare the pure h- and p-versions with the h-p-version on a geometric mesh and the adaptive h-p-version in solving both equations. The superiority of the combined versions (exponential convergence rate) on the pure versions (algebraic convergence rate) is emphasized. The numerical experiments are performed with the authors’ own code. The theoretical background consists of some important results many of them being the work of the second author. Reviewer: C.I.Gheorghiu (Cluj-Napoca) Cited in 26 Documents MSC: 65N38 Boundary element methods for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65R20 Numerical methods for integral equations 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35C15 Integral representations of solutions to PDEs 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) Keywords:numerical implementation; Laplace equation; h-p-version; h-version; p- version; Galerkin method; boundary element method; boundary integral equations; Symm’s integral equation; logarithmic kernel; hypersingular integral equation; exponential convergence rate; algebraic convergence rate; numerical experiments PDFBibTeX XMLCite \textit{F. V. Postell} and \textit{E. P. Stephan}, Comput. Methods Appl. Mech. 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