The Adaptive Crouzeix-Raviart Element Method For Convection-diffusion Eigenvalue Problems

The convection-diffusion eigenvalue problems have wide applications in fluid mechanics and energy science and so on,thus they have become a hot issue that many scholars are concerned about.In past years,the research of the a posteriori error of convectiondiffusion eigenvalue problems used to adopt the conforming finite element methods,but this paper first studies the adaptive algorithm of the Crouzeix-Raviart nonconforming element method for the convection-diffusion eigenvalue problems,gives the corresponding the a posteriori error estimates,and proves the reliability and efficiency of the a posteriori error estimators.Based on the a posteriori error estimators of this paper,in numerical experiments we propose an adaptive algorithm using the Crouzeix-Raviart element to solve the convectiondiffusion eigenvalue problems.And based on the work of Xu and Zhou,this paper proposes a two-grid discretization scheme using the Crouzeix-Raviart element to solve the problems.The numerical results validate the theoretical analysis and show that the algorithm and the two-grid discretization scheme presented in this paper are both efficient.Compared with the two-grid discretization using uniform refinements,the two-grid discretization using adaptive refinements can obtain eigenvalues with higher accuracy.