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 -

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.