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A High Order Galerkin Method for Integrals over Contour Lines with an Application to Plasma Physics

Drescher, Lukas ; Heumann, Holger ; Schmidt, Kersten :
A High Order Galerkin Method for Integrals over Contour Lines with an Application to Plasma Physics.
[Online-Edition: https://doi.org/10.1137/16M1102227]
In: SIAM Numer. Math., 55 (6) S. 2592-2615.
[Artikel] , (2017)

Offizielle URL: https://doi.org/10.1137/16M1102227

Kurzbeschreibung (Abstract)

We introduce a novel method to compute approximations of integrals over implicitly defined hypersurfaces. The new method is based on a weak formulation in L2(0,1) that uses the coarea formula to circumvent an explicit integration over the hypersurfaces. As such it is possible to use standard quadrature rules in the spirit of hp/spectral finite element methods, and the expensive computation of explicit hypersurface parametrizations is avoided. We derive error estimates showing that high order convergence can be achieved provided the integrand and the hypersurface defining function are sufficiently smooth. The theoretical results are supplemented by numerical experiments including an application for plasma modeling in nuclear fusion.

Typ des Eintrags: Artikel
Erschienen: 2017
Autor(en): Drescher, Lukas ; Heumann, Holger ; Schmidt, Kersten
Titel: A High Order Galerkin Method for Integrals over Contour Lines with an Application to Plasma Physics
Sprache: Englisch
Kurzbeschreibung (Abstract):

We introduce a novel method to compute approximations of integrals over implicitly defined hypersurfaces. The new method is based on a weak formulation in L2(0,1) that uses the coarea formula to circumvent an explicit integration over the hypersurfaces. As such it is possible to use standard quadrature rules in the spirit of hp/spectral finite element methods, and the expensive computation of explicit hypersurface parametrizations is avoided. We derive error estimates showing that high order convergence can be achieved provided the integrand and the hypersurface defining function are sufficiently smooth. The theoretical results are supplemented by numerical experiments including an application for plasma modeling in nuclear fusion.

Titel der Zeitschrift, Zeitung oder Schriftenreihe: SIAM Numer. Math.
Band: 55
(Heft-)Nummer: 6
Fachbereich(e)/-gebiet(e): 04 Fachbereich Mathematik
04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen
Hinterlegungsdatum: 19 Nov 2018 21:00
DOI: 10.1137/16M1102227
Offizielle URL: https://doi.org/10.1137/16M1102227
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