Error analysis of Petrov-Galerkin immersed finite element methods
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
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Detail(s)
Original language | English |
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Article number | 115744 |
Journal / Publication | Computer Methods in Applied Mechanics and Engineering |
Volume | 404 |
Online published | 28 Nov 2022 |
Publication status | Published - 1 Feb 2023 |
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DOI | DOI |
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Attachment(s) | Documents
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Link to Scopus | https://www.scopus.com/record/display.uri?eid=2-s2.0-85143678893&origin=recordpage |
Permanent Link | https://scholars.cityu.edu.hk/en/publications/publication(477d21b3-63f2-4b00-853d-ab1d202e5d10).html |
Abstract
This paper designs and analyzes a new and stable Petrov–Galerkin (PG) immersed finite element method (IFEM) for the second-order elliptic interface problems by introducing stabilization terms based on the classical PG-IFEM, which lacks the local positivity. The Petrov–Galerkin immersed finite element method uses the immersed finite element functions for the trial space and the standard finite element functions for the test space. Both the a priori and a posteriori error estimates of the method are analyzed in this paper. We prove the continuity and inf-sup condition and the a priori error estimate of the energy norm. The proposed a posteriori error estimator is proved to be both reliable and efficient, with both reliability and efficiency constants independent of the location of the interface. Extensive numerical results confirm the numerical scheme's optimal convergence and indicate the robustness with respect to the interface-mesh intersection and the coefficient contrast, despite the robustness of the inf-sup constant with respect to the interface-mesh intersection has yet been theoretically proved.
Research Area(s)
- A posteriori error estimates, A priori error estimates, Immersed finite element, Interface problems, Petrov–Galerkin
Citation Format(s)
Error analysis of Petrov-Galerkin immersed finite element methods. / He, Cuiyu; Zhang, Shun; Zhang, Xu.
In: Computer Methods in Applied Mechanics and Engineering, Vol. 404, 115744, 01.02.2023.
In: Computer Methods in Applied Mechanics and Engineering, Vol. 404, 115744, 01.02.2023.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review