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Solving two-dimensional H(curl)-elliptic interface systems with optimal convergence on unfitted meshes.
- Source :
-
European Journal of Applied Mathematics . Aug2023, Vol. 34 Issue 4, p774-805. 32p. - Publication Year :
- 2023
-
Abstract
- Finite element methods developed for unfitted meshes have been widely applied to various interface problems. However, many of them resort to non-conforming spaces for approximation, which is a critical obstacle for the extension to $\textbf{H}(\text{curl})$ equations. This essential issue stems from the underlying Sobolev space $\textbf{H}^s(\text{curl};\,\Omega)$ , and even the widely used penalty methodology may not yield the optimal convergence rate. One promising approach to circumvent this issue is to use a conforming test function space, which motivates us to develop a Petrov–Galerkin immersed finite element (PG-IFE) method for $\textbf{H}(\text{curl})$ -elliptic interface problems. We establish the Nédélec-type IFE spaces and develop some important properties including their edge degrees of freedom, an exact sequence relating to the $H^1$ IFE space and optimal approximation capabilities. We analyse the inf-sup condition under certain assumptions and show the optimal convergence rate, which is also validated by numerical experiments. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09567925
- Volume :
- 34
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- European Journal of Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 169713002
- Full Text :
- https://doi.org/10.1017/S0956792522000390