Geodesic
Exponential convergence of hp quadrature for integral operators with Gevrey kernels
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 3, pp. 387-422 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

Galerkin discretizations of integral equations in ℝ d require the evaluation of integrals I=∫ S (1) ∫ S (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 ≠ 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 𝒬 N using N function evaluations of g which achieves exponential convergence |I - 𝒬 N | ≤ C exp(-rNγ) with constants r, γ > 0.

DOI : 10.1051/m2an/2010061
Classification : 65N30
Keywords: numerical integration, hypersingular integrals, integral equations, Gevrey regularity, exponential convergence 
@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 },
     pages = {387--422},
     year = {2011},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {3},
     doi = {10.1051/m2an/2010061},
     zbl = {1269.65143},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010061/}
}
TY  - JOUR
AU  - Chernov, Alexey
AU  - von Petersdorff, Tobias
AU  - Schwab, Christoph
TI  - Exponential convergence of $hp$ quadrature for integral operators with Gevrey kernels
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2011
SP  - 387
EP  - 422
VL  - 45
IS  - 3
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010061/
DO  - 10.1051/m2an/2010061
LA  - en
ID  - M2AN_2011__45_3_387_0
ER  - 
%0 Journal Article
%A Chernov, Alexey
%A von Petersdorff, Tobias
%A Schwab, Christoph
%T Exponential convergence of $hp$ quadrature for integral operators with Gevrey kernels
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2011
%P 387-422
%V 45
%N 3
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010061/
%R 10.1051/m2an/2010061
%G en
%F 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 , Tome 45 (2011) no. 3, pp. 387-422. doi: 10.1051/m2an/2010061

Cité par Sources :