Coefficient Jump-Independent Approximation of the Conforming and Nonconforming Finite Element Solutions (Advances in Applied Mathematics and Mechanics, 2018)
A counterexample is constructed. It confirms that the error of conformingfinite element solution is proportional to the coefficient jump, when solving interfaceelliptic equations. The Scott-Zhang operator is applied to a nonconforming finite element.It is shown that the nonconforming finite element provides the optimal orderapproximation in interpolation, in $L^2$-projection, and in solving elliptic differential equation,independent of the coefficient jump in the elliptic differential equation. Numericaltests confirm the theoretical finding.