## A posteriori error estimates in Adini finite element for eigenvalue problems.(English)Zbl 0957.65092

Author’s abstract: We discuss a posteriori error estimates of the eigenvalue $$\lambda_h$$ given by the Adini nonconforming finite element method. We give an asymptotically exact error estimator of the $$\lambda_h$$. We prove that the order of convergence of the $$\lambda_h$$ is just 2 and the $$\lambda_h$$ converge form below for sufficiently small $$h$$.

### MSC:

 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35P15 Estimates of eigenvalues in context of PDEs