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dc.contributor.author
Chernov, Alexey
dc.contributor.author
von Petersdorff, Tobias
dc.contributor.author
Schwab, Christoph
dc.date.accessioned
2022-09-02T12:58:37Z
dc.date.available
2017-06-09T11:00:28Z
dc.date.available
2022-09-02T12:58:37Z
dc.date.issued
2011-05
dc.identifier.issn
2822-7840
dc.identifier.issn
2804-7214
dc.identifier.other
10.1051/m2an/2010061
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/34742
dc.description.abstract
Galerkin discretizations of integral equations in $ \mathbb{R}^d$ require the evaluation of integrals $ I = \int_{S^{{(1)}}}$ $\int_{S^{{(2)}}}$ $g(x,y)dydx$ where $S^{{(1)}}, S^{{(2)}}$ are $d$-simplices and $g$ has a singularity at $x = y$. We assume that $g$ is Gevrey smooth for $x \neq y$ 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 $Q_N$ usin $N$ function evaluations of $g$ which achieves exponential convergence | $ I - Q_N$ | $\leq C$ exp$(-rN^{\gamma})$ with constants $r, \gamma$ > 0.
en_US
dc.language.iso
en
en_US
dc.publisher
EDP Sciences
en_US
dc.subject
Numerical integration
en_US
dc.subject
hypersingular integrals
en_US
dc.subject
integral equations
en_US
dc.subject
Gevrey regularity
en_US
dc.subject
exponential convergence
en_US
dc.title
Exponential convergence of $hp$ quadrature for integral operators with Gevrey kernels
en_US
dc.type
Journal Article
dc.date.published
2010-10-11
ethz.journal.title
ESAIM: Mathematical Modelling and Numerical Analysis
ethz.journal.volume
45
en_US
ethz.journal.issue
3
en_US
ethz.journal.abbreviated
ESAIM: M2AN
ethz.pages.start
387
en_US
ethz.pages.end
422
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Les Ulis
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
ethz.relation.isNewVersionOf
10.3929/ethz-a-010406066
ethz.date.deposited
2017-06-09T11:01:00Z
ethz.source
ECIT
ethz.identifier.importid
imp59364e04c33af46006
ethz.ecitpid
pub:55956
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2017-07-12T20:36:30Z
ethz.rosetta.lastUpdated
2018-10-01T12:38:48Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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