TY - JOUR
T1 - Superconvergence and Flux Recovery for an Enriched Finite Element Method
AU - Attanayake , Champike
AU - Chou , So-Hsiang
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 656
EP - 673
PY - 2021
DA - 2021/08
SN - 18
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/19387.html
KW - Flux recovery technique, superconvergence, enriched finite element, immersed finite element method.
AB - <p style="text-align: justify;">We introduce a flux recovery scheme for an enriched finite element method applied
to an interface diffusion equation with absorption. The method is a variant of the finite element
method introduced by Wang $et$ $al$. in [20]. The recovery is done at nodes first and then extended to
the whole domain by interpolation. In the case of piecewise constant diffusion coefficient, we show
that the nodes of the finite elements are superconvergence points for both the primary variable $p$ and its flux $u$. In particular, in the absence of the absorption term zero error is achieved at the
nodes and interface point in the approximation of $u$ and $p$. In the general case, pressure error
at the nodes and interface point is second order. Numerical results are provided to confirm the
theory.</p>