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Carstensen, C. and Bartels, S. (2002) Each Averaging Technique Yields Reliable a Posteriori Error Control in FEM on Unstructured Grids. Part1: Low Order Conforming, Nonconforming, and Mixed FEM. Mathematics of Computation, 71, 945-969.
https://doi.org/10.1090/S0025-5718-02-01402-3

has been cited by the following article:

• TITLE: A Posteriori Error Estimate of Two Grid Mixed Finite Element Methods for Semilinear Elliptic Equations

  AUTHORS: Yiming Wen, Luoping Chen, Jiajia Dai

  KEYWORDS: Two-Grid Mixed Finite Element Methods, Posteriori Error Estimates, Semilinear Elliptic Equations, Averaging Technique

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.2, February 7, 2023

  ABSTRACT: In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.