A locally modified second-order finite element method for interface problems

Frei, Stefan; Judakova, Gozel; Richter, Thomas

A locally modified second-order finite element method for interface problems

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2020

Autor:innen

Frei, Stefan

Judakova, Gozel

Richter, Thomas

ArXiv-ID

http://arxiv.org/abs/2007.13906

Sammlungen

Mathematik und Statistik

Publikationstyp

Preprint

Publikationsstatus

Published

Zusammenfassung

The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334] is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is based on a fixed structured coarse mesh, which is then refined into sub-elements to resolve an interior interface. In this work, we extend the locally modified finite element method to second order using an isoparametric approach in the interface elements. Thereby we need to take care that the resulting curved edges do not lead to degenerate sub-elements. We prove optimal a priori error estimates in the L²-norm and in a modified energy norm, as well as a reduced convergence order of O(h³/²) in the standard H¹-norm. Finally, we present numerical examples to substantiate the theoretical findings.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

FREI, Stefan, Gozel JUDAKOVA, Thomas RICHTER, 2020. A locally modified second-order finite element method for interface problems

BibTex

@unpublished{Frei2020-07-27T23:08:48Zlocal-55628,
  year={2020},
  title={A locally modified second-order finite element method for interface problems},
  author={Frei, Stefan and Judakova, Gozel and Richter, Thomas}
}

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