1 results
Exponential convergence of hp quadraturefor integral operators with Gevrey kernels
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- Journal:
- ESAIM: Mathematical Modelling and Numerical Analysis / Volume 45 / Issue 3 / May 2011
- Published online by Cambridge University Press:
- 11 October 2010, pp. 387-422
- Print publication:
- May 2011
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- Article
- Export citation
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Galerkin discretizations of integral equations in $\mathbb{R}^{d}$
requirethe evaluation of integrals $I = \int_{S^{(1)}}\int_{S^{(2)}}g(x,y){\rm d}y{\rm d}x$ 
where S (1),S (2) are d-simplices and g has a singularityat x = y. We assume that g is Gevrey smooth for x $\ne$ 
y andsatisfies bounds for the derivatives which allow algebraic singularitiesat x = y. This holds for kernel functions commonly occurring in integralequations. We construct a family of quadrature rules $\mathcal{Q}_{N}$ 
usingN function evaluations of g which achieves exponential convergence|I – $\mathcal{Q}_{N}$ | ≤C exp(–r N γ ) with constants r, γ > 0.
