TY - JOUR
T1 - Coefficient Jump-Independent Approximation of the Conforming and Nonconforming Finite Element Solutions
AU - Zhang , Shangyou
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 722
EP - 736
PY - 2018
DA - 2018/05
SN - 8
DO - http://doi.org/10.4208/aamm.2015.m931
UR - https://global-sci.org/intro/article_detail/aamm/12112.html
KW - Jump coefficient, finite element, $L^2$ projection, weighted projection, Scott-Zhang operator.
AB - <p style="text-align: justify;">A counterexample is constructed. It confirms that the error of conforming
finite element solution is proportional to the coefficient jump, when solving interface
elliptic equations. The Scott-Zhang operator is applied to a nonconforming finite element.
It is shown that the nonconforming finite element provides the optimal order
approximation in interpolation, in $L^2$-projection, and in solving elliptic differential equation,
independent of the coefficient jump in the elliptic differential equation. Numerical
tests confirm the theoretical finding.</p>