Residual-based a Posteriori Error Estimate for Interface Problems:   Nonconforming Linear Elements
  In this paper, we study a modified residual-based a posteriori error estimator for the nonconforming linear finite element approximation to the interface problem. The reliability of the estimator is analyzed by a new and direct approach without using the Helmholtz decomposition. It is proved that the estimator is reliable with constant independent of the jump of diffusion coefficients across the interfaces, without the assumption that the diffusion coefficient is quasi-monotone. Numerical results for one test problem with intersecting interfaces are also presented. 
Zhiqiang Cai, Cuiyu He, Shun Zhang
math.NA