A High Order Method for the Approximation of Integrals Over Implicitly Defined Hypersurfaces

Abstract : We introduce a novel method to compute approximations of integrals over implicitly defined hyper-surfaces. The new method is based on a weak formulation in L 2 (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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [31 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01637946
Contributor : Holger Heumann <>
Submitted on : Saturday, November 18, 2017 - 6:13:22 PM
Last modification on : Friday, July 20, 2018 - 1:42:02 PM
Long-term archiving on : Monday, February 19, 2018 - 12:28:37 PM

File

HeumannDrescherSchmidt_16v4.pd...
Files produced by the author(s)

Identifiers

Citation

Lukas Drescher, Holger Heumann, Kersten Schmidt. A High Order Method for the Approximation of Integrals Over Implicitly Defined Hypersurfaces. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2017, 55 (6), pp.2592 - 2615. ⟨10.1137/16M1102227⟩. ⟨hal-01637946⟩

Share

Metrics

Record views

190

Files downloads

266