A sharp interface method using enriched finite elements for elliptic interface problems
- We present an immersed boundary method for the solution of elliptic interface problems with discontinuous coefficients which provides a second-order approximation of the solution. The proposed method can be categorised as an extended or enriched finite element method. In contrast to other extended FEM approaches, the new shape functions get projected in order to satisfy the Kronecker-delta property with respect to the interface. The resulting combination of projection and restriction was already derived in Höllbacher and Wittum (TBA, 2019a) for application to particulate flows. The crucial benefits are the preservation of the symmetry and positive definiteness of the continuous bilinear operator. Besides, no additional stabilisation terms are necessary. Furthermore, since our enrichment can be interpreted as adaptive mesh refinement, the standard integration schemes can be applied on the cut elements. Finally, small cut elements do not impair the condition of the scheme and we propose a simple procedure to ensure good conditioning independent of the location of the interface. The stability and convergence of the solution will be proven and the numerical tests demonstrate optimal order of convergence.
Author: | Susanne HöllbacherGND, Gabriel WittumGND |
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URN: | urn:nbn:de:hebis:30:3-636845 |
DOI: | https://doi.org/10.1007/s00211-021-01180-0 |
ISSN: | 0945-3245 |
Parent Title (English): | Numerische Mathematik |
Publisher: | Springer |
Place of publication: | Berlin ; Heidelberg |
Document Type: | Article |
Language: | English |
Date of Publication (online): | 2021/03/02 |
Date of first Publication: | 2021/03/02 |
Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
Release Date: | 2022/10/21 |
Volume: | 147 |
Issue: | 4 |
Page Number: | 23 |
First Page: | 759 |
Last Page: | 781 |
Note: | Open Access funding enabled and organized by Projekt DEAL. |
HeBIS-PPN: | 50514638X |
Institutes: | Wissenschaftliche Zentren und koordinierte Programme / Goethe-Zentrum für Wissenschaftliches Rechnen (G-CSC) |
Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik | |
MSC-Classification: | 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Axx General topics / 35A15 Variational methods |
Sammlungen: | Universitätspublikationen |
Licence (German): | Creative Commons - Namensnennung 4.0 |