A recovery-based error estimate for nonconforming finite volume methods of interface problems

In Cai and Zhang (2009, 2010) [12,13], they introduced the recovery-based a posteriori error estimator for conforming, mixed, and nonconforming finite element methods of interface problems. In this paper, we extend the idea to present a recovery-based a posterior error estimator for finite volume methods which employ the nonconforming linear trial functions to approximate elliptic interface problems. The method recovers the flux and gradient in H(div) and H(curl) conforming finite element spaces with a weighted L2 projection, respectively. The reliability and efficiency bounds are established. Numerical experiments are given to support the conclusions.