Exponential convergence of hp quadrature for integral operators with Gevrey kernels
Hausdorff Center for Mathematics and Institute for Numerical Simulation, University of Bonn,
Endenicher Allee 60, 53115 Bonn, Germany.
2 Department of Mathematics, University of Maryland, College Park, MD 20742, USA.
3 Seminar für Angewandte Mathematik, ETH Zürich, 8092 Zürich, Switzerland. email@example.com
Galerkin discretizations of integral equations in require the evaluation of integrals where S(1),S(2) are d-simplices and g has a singularity at x = y. We assume that g is Gevrey smooth for x y and satisfies bounds for the derivatives which allow algebraic singularities at x = y. This holds for kernel functions commonly occurring in integral equations. We construct a family of quadrature rules using N function evaluations of g which achieves exponential convergence |I – | ≤ C exp(–rNγ) with constants r, γ > 0.
Mathematics Subject Classification: 65N30
Key words: Numerical integration / hypersingular integrals / integral equations / Gevrey regularity / exponential convergence
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