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.
@article{M2AN_2011__45_3_387_0,
author = {Chernov, Alexey and von Petersdorff, Tobias and Schwab, Christoph},
title = {Exponential convergence of $hp$ quadrature for integral operators with Gevrey kernels},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {45},
year = {2011},
pages = {387-422},
doi = {10.1051/m2an/2010061},
zbl = {1269.65143},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2011__45_3_387_0}
}
Chernov, Alexey; von Petersdorff, Tobias; Schwab, Christoph. Exponential convergence of $hp$ quadrature for integral operators with Gevrey kernels. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 45 (2011) pp. 387-422. doi : 10.1051/m2an/2010061. http://gdmltest.u-ga.fr/item/M2AN_2011__45_3_387_0/
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