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Exponential Convergence of Gauss--Jacobi Quadratures for Singular Integrals over Simplices in Arbitrary Dimension

Chernov, Alexey ; Schwab, Christoph

SIAM Journal on Numerical Analysis, 2012, pp.1433-1455 [Peer Reviewed Journal]

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Title:
Exponential Convergence of Gauss--Jacobi Quadratures for Singular Integrals over Simplices in Arbitrary Dimension
Author/Creator: Chernov, Alexey ; Schwab, Christoph
Language: English
Subjects: Gauss–Jacobi Quadrature ; Numerical Integration ; High Dimensional Integrands ; Hypersingular Integrals ; Integral Equations ; Gevrey Regularity ; Exponential Convergence
Is Part Of: SIAM Journal on Numerical Analysis, 2012, pp.1433-1455
Description: Galerkin discretizations of integral operators in $\mathbb{R}^{d}$ require the evaluation of integrals $\int_{S^{(1)}}\!\int_{S^{(2)}}\!f(x,y)\,dydx$, where $S^{(1)},S^{(2)}$ are $d$-dimensional simplices and $f$ has a singularity at $x=y$. In [A. Chernov, T. von Petersdorff, and C. Schwab, M$2$AN Math....
Identifier: ISSN: 00361429 ; E-ISSN: 10957170 ; DOI: 10.1137/100812574

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