Recovery-Based Error Estimators for Interface Problems: Mixed and Nonconforming Finite Elements
SIAM Journal on Numerical Analysis
Flux Recovery and A Posteriori Error Estimators: Conforming Elements for Scalar Elliptic Equations
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Robust Equilibrated Residual Error Estimator for Diffusion Problems: Conforming Elements
SIAM Journal on Numerical Analysis
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
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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.