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.