The adaptive Crouzeix-Raviart element method for convection-diffusion eigenvalue problems

TL;DR

This paper develops an adaptive Crouzeix-Raviart element method with a posteriori error estimators for convection-diffusion eigenvalue problems, demonstrating its efficiency through theoretical analysis and numerical validation.

Contribution

It introduces a new adaptive nonconforming element method with proven reliable and efficient a posteriori error estimators for convection-diffusion eigenvalue problems.

Findings

The a posteriori error estimators are reliable and efficient.

Numerical results confirm the theoretical analysis.

The adaptive algorithm improves computational efficiency.

Abstract

The convection-diffusion eigenvalue problems are hot topics, and computational mathematics community and physics community are concerned about them in recent years. In this paper, we consider the a posteriori error analysis and the adaptive algorithm of the Crouzeix-Raviart nonconforming element method for the convection-diffusion eigenvalue problems. We give the corresponding a posteriori error estimators, and prove their reliability and efficiency. Finally, the numerical results validate the theoretical analysis and show that the algorithm presented in this paper is efficient.