Isoparametric finite-element approximation of a Steklov eigenvalue problem

A two-grid discretization scheme for the Steklov eigenvalue problem

“…Consider the source problem (4) associated with (2) and the approximate source problem (5) associated with (3)…”

“…For instance, they are found in the study of surface waves (see [7]), in the analysis of stability of mechanical oscillators immersed in a viscous fluid (see [14] and the references therein), and in the study of the vibration modes of a structure in contact with an incompressible fluid (see, for example, [8]). Numerical methods of Steklov eigenvalue problems have been developed, and the optimal error estimates have been obtained (see [2,9,19,26] and the references therein). Huang and Lü [17] analyzed extrapolation for solving BIE of Steklov eigenvalue problems and Li, Lin and Zhang [18] analyzed the extrapolation and superconvergence of the Steklov eigenvalue problem in order to improve numerical approximation accuracy.…”

Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations

“…The analysis of the conforming finite element methods for the Steklov eigenvalue problems has been given by Bramble and Osborn [12], Andreev and Todorov [3].…”

A two-grid method of the non-conforming Crouzeix–Raviart element for the Steklov eigenvalue problem

“…Bramble and Osborn [6] studied the Galerkin method for the approximation of Steklov eigenvalue problem of non-selfadjoint second order elliptic operators. Andreev and Todorov [3] discussed the isoparametric finite element method for the approximation of the Steklov eigenvalue problem of second order selfadjoint elliptic differential operators. Armentano and Padra [4] proposed and analyzed an a posteriori error estimator, of the residual type, for the linear finite element approximation of the Steklov eigenvalue problem.…”