TY - JOUR
T1 - High Degree Immersed Finite Element Spaces by a Least Squares Method
JO - International Journal of Numerical Analysis and Modeling
VL - 4-5
SP - 604
EP - 626
PY - 2017
DA - 2017/08
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10052.html
KW - Interface problems, discontinuous coefficients, finite element spaces, curved interfaces, higher order.
AB - <p style="text-align: justify;">We present a least squares framework for constructing $p$-th degree immersed finite
element (IFE) spaces for typical second-order elliptic interface problems. This least squares formulation
enforces interface jump conditions including extended ones already proposed in the
literature, and it guarantees the existence of $p$-th IFE shape functions on interface elements. The
uniqueness of the proposed $p$-th degree IFE shape functions is also discussed. Computational results
are presented to demonstrate the approximation capabilities of the proposed $p$-th IFE spaces
as well as other features.</p>