Author(s)

Yiming Wen, Luoping Chen^*, Jiajia Dai

School of Mathematics, Southwest Jiaotong University, Chengdu, China.

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.

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

Wen, Y. , Chen, L. and Dai, J. (2023) A Posteriori Error Estimate of Two Grid Mixed Finite Element Methods for Semilinear Elliptic Equations. Journal of Applied Mathematics and Physics, 11, 361-376. doi: 10.4236/jamp.2023.112020.