Year: 2014
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 3 : pp. 541–566
Abstract
We present higher degree immersed finite element (IFE) spaces that can be used to solve two dimensional second order elliptic interface problems without requiring the mesh to be aligned with the material interfaces. The interpolation errors in the proposed piecewise $p^{th}$ degree spaces yield optimal $\mathcal{O}(h^{p+1})$ and $\mathcal{O}(h^p)$ convergence rates in the $L^2$ and broken $H^1$ norms, respectively, under mesh refinement. A partially penalized method is developed which also converges optimally with the proposed higher degree IFE spaces. While this penalty is not needed when either linear or bilinear IFE space is used, a numerical example is presented to show that it is necessary when a higher degree IFE space is used.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2014-IJNAM-541
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 3 : pp. 541–566
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Immersed finite element immersed interface interface problems Cartesian mesh method structured mesh higher degree finite element.