## A note about nonconforming finite element approximations of the Steklov eigenvalue problem.(Chinese. English summary)Zbl 1212.65435

Summary: This paper explores nonconforming finite element approximations of the Steklov eigenvalue problem where $$\varOmega$$ is a bounded concave polygonal domain. Numerical results show that the approximate eigenvalues derived from the nonconforming Crouzeix-Raviart element, the $$Q^{\mathrm{rot}}_1$$ element and the $$EQ^{\mathrm{rot}}_1$$ element have the same convergence order as that obtained from the piecewise linear conforming finite element and provide lower bounds for the exact eigenvalues.

### MSC:

 65N25 Numerical methods for eigenvalue problems 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 65N15 Error bounds for boundary value problems involving PDEs