Abstract
In [Z. Cai and S. Zhang, SIAM J. Numer. Anal., 47 (2009), pp. 2132–2156], we introduced and analyzed a recovery-based a posteriori error estimator for conforming linear finite element approximation to interface problems. It was shown theoretically that the estimator is robust with respect to the size of jumps provided that the distribution of coefficients is locally monotone. Numerical examples showed that this condition is unnecessary. This paper extends the idea in [Z. Cai and S. Zhang, SIAM J. Numer. Anal., 47 (2009), pp. 2132–2156] to mixed and nonconforming finite element methods for developing and analyzing robust estimators. Numerical results on test problems are also presented. Moreover, an a priori error estimate is obtained when the underlying problem has low regularity.
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