@Article{AAMM-8-722, author = {Zhang , Shangyou}, title = {Coefficient Jump-Independent Approximation of the Conforming and Nonconforming Finite Element Solutions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {5}, pages = {722--736}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m931}, url = {http://global-sci.org/intro/article_detail/aamm/12112.html} }