TY - JOUR
T1 - Flux Recovery and Superconvergence of Quadratic Immersed Interface Finite Elements
AU - S.-H. Chou & C. Attanayake
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 88
EP - 102
PY - 2016
DA - 2016/01
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/412.html
KW - Recovery technique, quadratic immersed interface method, Superconvergence, conservative method, Green's function.
AB - <p style="text-align: justify;">We introduce a flux recovery scheme for the computed solution of a quadratic immersed
finite element method introduced by Lin et al. in [13]. The recovery is done at nodes
and interface point first and by interpolation at the remaining points. In the case of piecewise
constant diffusion coefficient, we show that the end nodes are superconvergence points for both
the primary variable $p$ and its flux $u$. Furthermore, in the case of piecewise constant diffusion
coefficient without the absorption term the errors at end nodes and interface point in the approximation
of $u$ and $p$ are zero. In the general case, flux error at end nodes and interface point is
third order. Numerical results are provided to confirm the theory.</p>