Quadrature for \(hp\)-Galerkin BEM in \({\hbox{\sf l\kern-.13em R}}^3\)


The Galerkin discretization of a Fredholm integral equation of the second kind on a closed, piecewise analytic surface \(\Gamma \subset \hbox{\sf l\kern-.13em R}^3\) is analyzed. High order, \(hp\)-boundary elements on grids which are geometrically graded toward the edges and vertices of the surface give exponential convergence, similar to what is known in the \(hp\)-Finite Element Method. A quadrature strategy is developed which gives rise to a fully discrete scheme preserving the exponential convergence of the \(hp\)-Boundary Element Method. The total work necessary for the consistent quadratures is shown to grow algebraically with the number of degrees of freedom. Numerical results on a curved polyhedron show exponential convergence with respect to the number of degrees of freedom as well as with respect to the CPU-time.

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Received April 22, 1996

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Sauter, S., Schwab, C. Quadrature for \(hp\)-Galerkin BEM in \({\hbox{\sf l\kern-.13em R}}^3\) . Numer. Math. 78, 211–258 (1997). https://doi.org/10.1007/s002110050311

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  • Mathematics Subject Classification (1991):65N38; 65N55