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Exponential convergence of hp quadrature for integral operators with Gevrey kernels

by A. Chernov and T. von Petersdorff and Ch. Schwab

(Report number 2009-03)

Abstract
Galerkin discretizations of integral equations in Rd require the evaluation of integrals I=RS(1) RS(2) g(x,y)dydx 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 6=y and satisfies bounds for the derivatives which allow algebraic singularities at x=y. This holds for kernel functions commonly occuring in integral equations. We construct a family of quadrature rules QN using N function evaluations of g which achieves exponential convergence (I-YN)0.

Keywords:

@Techreport{CvS09_56,
  author = {A. Chernov and T. von Petersdorff and Ch. Schwab},
  title = {Exponential convergence of hp quadrature for integral operators with Gevrey kernels},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2009-03},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2009/2009-03.pdf },
  year = {2009}
}

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