TY - JOUR
T1 - Higher Degree Immersed Finite Element Methods for Second-Order Elliptic Interface Problems
AU - S. Adjerid, M. Ben-Romdhane & T. Lin
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 541
EP - 566
PY - 2014
DA - 2014/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/541.html
KW - Immersed finite element, immersed interface, interface problems, Cartesian mesh method, structured mesh, higher degree finite element.
AB - <p style="text-align: justify;">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.</p>