Isoparametric Finite Element Approximation of Steklov Eigenvalue Problem
by
Andrey Borissov Andreev
Department of Mathematics,Technical University of Gabrovo,Bulgaria & Central Laboratory for Parallel Processing,Bulgarian Academy of Sciences, Sofia.
Coauthors: Todor Dimitrov Todorov (Department of Mathematics, Technical University of Gabrovo,Bulgaria)

In this paper we study the isoparametric variant of finite element method (FEM) for the approximation of Steklov eigenvalue problem for second-order, selfadjoint, strongly elliptic partial differential operators. Error estimates for eigenfunctions and eigenvalues are derived. We prove the same estimate for eigenvalues as the one obtained in the case of conforming finite elements provided the boundary of the domain is well approximated. Some algorithmic aspects arising from the FE isoparametric discretization of Steklov problem are analyzed.

Date received: February 18, 2000