Coefficient Jump-Independent Approximation of the Conforming and Nonconforming Finite Element Solutions
Shangyou Zhang
10.4208/aamm.2015.m931
Adv. Appl. Math. Mech., 8 (2016), pp. 722-736.
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 L2-projection, and in solving elliptic differential equation,
independent of the coefficient jump in the elliptic differential equation. Numerical
tests confirm the theoretical finding.
