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Diedrich, C., Dijkstra, D., Hamaekers, J., Henninger, B. and Randrianarivony, M. (2015) A Finite Element Study on the Effect of Curvature on the Reinforcement of Matrices by Randomly Distributed and Curved Nanotubes. Journal of Computational and Theoretical Nanoscience, 12, 2108-2116. https://doi.org/10.1166/jctn.2015.3995

has been cited by the following article:

• TITLE: Error Estimator Using Higher Order FEM for an Interface Problem

  AUTHORS: Maharavo Randrianarivony

  KEYWORDS: Estimator, A-Posteriori, Interface, Transmission, Higher Order, FEM, Residual

  JOURNAL NAME: Applied Mathematics, Vol.8 No.12, December 18, 2017

  ABSTRACT: A higher order finite element method is considered to treat an interface problem. The polynomial degree is allowed to be arbitrary but it is fixed for the FEM-variational formulation. We propose an error estimator which turns out to be efficient and reliable. We demonstrate upper and lower bounds of the error estimator with respect to the exact accuracy. For the transmission problem, the coefficients for the internal and external domains can be highly dissimilar. One major difficulty is the characteristic of the estimator at the interface. The a-posteriori error estimates can be computed very efficiently element by element. To corroborate the theoretical analysis, we report on a few numerical results.