| Issue |
ESAIM: M2AN
Volume 57, Number 6, November-December 2023
|
|
|---|---|---|
| Page(s) | 3615 - 3636 | |
| DOI | https://doi.org/10.1051/m2an/2023078 | |
| Published online | 20 December 2023 | |
A nonconforming immersed virtual element method for elliptic interface problems
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 34141, South Korea
* Corresponding author: kdy@kaist.ac.kr
Received:
27
February
2023
Accepted:
12
September
2023
This paper presents the lowest-order nonconforming immersed virtual element method for solving elliptic interface problems on unfitted polygonal meshes. The local discrete space on each interface mesh element consists of the solutions of local interface problems with Neumann boundary conditions, and the elliptic projection is modified so that its range is the space of broken linear polynomials satisfying the interface conditions. We derive optimal error estimates in the broken H1-norm and L2-norm, under the piecewise H2-regulartiy assumption. In our scheme, the mesh assumptions for error analysis allow small cut elements. Several numerical experiments are provided to confirm the theoretical results.
Mathematics Subject Classification: 65N12 / 65N15 / 65N30
Key words: Immersed virtual element method / nonconforming method / elliptic interface problem / unfitted mesh / polygonal mesh
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.