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Durango, F. and Novo, J. (2019) A Posteriori Error Estimations for Mixed Finite Element Approximations to the Navier-Stokes Equations Based on Newton-Type Linearization. Journal of Computational and Applied Mathematics, 367, Article ID: 112429.
https://doi.org/10.1016/j.cam.2019.112429

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.