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

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

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.

Item Type: Article
Erschienen: 2017
Creators: Drescher, Lukas and Heumann, Holger and Schmidt, Kersten
Title: A High Order Galerkin Method for Integrals over Contour Lines with an Application to Plasma Physics
Language: English
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.

Journal or Publication Title: SIAM Numer. Math.
Volume: 55
Number: 6
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 19 Nov 2018 21:00
DOI: 10.1137/16M1102227
Official URL: https://doi.org/10.1137/16M1102227
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