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

A Multi-Level Mixed Element Method for the Eigenvalue Problem of Biharmonic Equation

“…The idea of the two-grid method is related to the ideas in [23,24] for nonsymmetric or indefinite problems and nonlinear elliptic equations. Since then, many numerical 1 methods for solving eigenvalue problems based on the idea of the two-grid method are developed (see, e.g., [5,12,14,28,34,42]). A type of multi-level correction scheme is presented by LinXie [33] and Xie [40].…”

Numerical studies of the Steklov eigenvalue problem via conformal mappings

“…Therefore, we get (15) where κ is the mean curvature. Now consider the optimization problem (13) and use the shape derivative of λ, we get…”

Spectral Galerkin approximation and rigorous error analysis for the Steklov eigenvalue problem in circular domain

“…There are various approximate methods for solving the Steklov eigenvalue problems. Andreev and Todorov 7 discussed the isoparametric finite element method (FEM); Armentano and Padra 8 introduced and analyzed the conforming linear finite element approximation of the Steklov eigenvalue problem in a bounded polygonal domain; Alonso and Russo, 9 Yang et al, 10 and Li et al 11 studied nonconforming finite elements approximation; Li and Yang 12 and Bi and Yang 13 discussed a 2-grid method of the conforming and nonconforming FEM, respectively; Li et al 14 studied the extrapolation and superconvergence of the Steklov eigenvalue problem; Tang et al 15 studied the boundary element approximation; Bi and Yang 16 discussed the multiscale discretization scheme on the basis of the Rayleigh quotient iterative method; Garau and Morin 17 analyzed the convergence and quasi-optimality of adaptive FEM for Steklov eigenvalue problems; Cao et al 18 discussed the multiscale asymptotic method for Steklov eigenvalue equations in composite media; Zhang et al 19 discussed the spectral method with the tensor-product nodal basis for the Steklov eigenvalue problem in rectangular domain.…”