Isoparametric finite-element approximation of a Steklov eigenvalue problem

We study the isoparametric variant of the finite-element method (FEM) for an approximation of Steklov eigenvalue problems for second-order, selfadjoint, elliptic differential operators. Error estimates for eigenfunctions and eigenvalues are derived. We prove the same estimate for eigenvalues as that obtained in the case of conforming finite elements provided that the boundary of the domain is well approximated. Some algorithmic aspects arising from the FE isoparametric discretization of the Steklov problems are analysed. We finish this paper with numerical results confirming the considered theory.