Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations. (English) Zbl 1274.65296

The authors consider the Steklov eigenvalue problem given by a second-order elliptic equation in a two-dimensional bounded polygonal domain and a Neumann-type boundary condition containing the eigenvalue \(\lambda\). They use four kinds of nonconforming finite elements for its numerical approximation. The main theorem establishes an optimal rate of convergence of the associated normed eigenfunctions on convex and also non-convex domains. Guaranteed lower bounds of particular eigenvalues are derived as well. Numerical tests nicely illustrate the theoretical rate of convergence of the eigenvalues on the L-shape domain.
Reviewer: Michal Krizek


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
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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