33 citations · 47 across the 16 of their papers we have counts for
16 papers
A high order stabilization-free virtual element method for general second-order elliptic eigenvalue problem
Liangkun Xu, Shixi Wang, Yidu Yang +1
In this paper, we discuss a novel higher-order stabilization-free virtual element method for general second-order elliptic eigenvalue problems. Optimal a priori error estimates are…
The discontinuous Galerkin method for the Oseen eigenvalue problem
Lingling Sun, Shixi Wang, Hai Bi +1
In this paper, we focus on investigating symmetric and nonsymmetric discontinuous Galerkin (DG) methods for solving the Oseen eigenvalue problem based on the velocity-pressure form…
A locking-free discontinuous Galerkin method for linear elastic Steklov eigenvalue problem
Yanjun Li, Hai Bi
In this paper, a discontinuous Galerkin finite element method of Nitsche's version for the Steklov eigenvalue problem in linear elasticity is presented. The a priori error estimate…
The a posteriori error estimates and an adaptive algorithm of the FEM for transmission eigenvalues for anisotropic media
Shixi Wang, Hai Bi, Yidu Yang
The transmission eigenvalue problem arising from the inverse scattering theory is of great importance in the theory of qualitative methods and in the practical applications. In thi…
A posteriori error estimates of mixed discontinuous Galerkin method for the Stokes eigenvalue problem
L. L. Sun, H. Bi, Y. D. Yang
In this paper, for the Stokes eigenvalue problem in -dimensional case , we present an a posteriori error estimate of residual type of the mixed discontinuous Galerkin f…
The nonconforming Crouzeix-Raviart element approximation and two-grid discretizations for the elastic eigenvalue problem
Hai Bi, Xuqing Zhang, Yidu Yang
In this paper, we extend the work of Brenner and Sung [Math. Comp. 59, 321--338 (1992)] and present a regularity estimate for the elastic equations in concave domains. Based on the…
Lower bounds for eigenvalues of the Steklov eigenvalue problem with variable coefficients
Yu Zhang, Hai Bi, Yidu Yang
In this paper, using new correction to the Crouzeix-Raviart finite element eigenvalue approximations, we obtain lower eigenvalue bounds for the Steklov eigenvalue problem with vari…
Non-conforming Crouzeix-Raviar element approximation for Stekloff eigenvalues in inverse scattering
Yidu Yang, Yu Zhang, Hai Bi
In this paper, we use the non-conforming Crouzeix-Raviart element method to solve a Stekloff eigenvalue problem arising in inverse scattering. The weak formulation corresponding to…
A multigrid correction scheme for a new Steklov eigenvalue problem in inverse scattering
Yu Zhang, Hai Bi, Yidu Yang
We propose a multigrid correction scheme to solve a new Steklov eigenvalue problem in inverse scattering. With this scheme, solving an eigenvalue problem in a fine finite element s…
Two-grid discretizations and a local finite element scheme for a non-selfadjoint Stekloff eigenvalue problem
Hai Bi, Yu Zhang, Yidu Yang
In this paper, for a new Stekloff eigenvalue problem which is non-selfadjoint and not -elliptic, we establish and analyze two kinds of two-grid discretization scheme and a loc…
New error estimates of linear triangle finite elements for the Steklov eigenvalue problem
Hai Bi, Yidu Yang, Yuanyuan Yu
In this paper we make a further discussion on the finite elements approximation for the Steklov eigenvalue problem on concave polygonal domain. We make full use of the regularity e…
A New Multigrid Finite Element Method for the Transmission Eigenvalue Problems
Jiayu Han, Yidu Yang, Hai Bi
Numerical methods for the transmission eigenvalue problems are hot topics in recent years. Based on the work of Lin and Xie [Math. Comp., 84(2015), pp. 71-88], we build a multigrid…
An adaptive algorithm based on the shifted inverse iteration for the Steklov eigenvalue problem
Hai Bi, Hao Li, Yidu Yang
This paper proposes and analyzes an a posteriori error estimator for the finite element multi-scale discretization approximation of the Steklov eigenvalue problem. Based on the a p…
Non-conforming finite element methods for transmission eigenvalue problem
Yidu Yang, Jiayu Han, Hai Bi
The transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering theory. In this paper, for the Helmholtz transmission eigenvalue problem…
The lower bound property of the Morley element eigenvalues
Yidu Yang, Hao Li, Hai Bi
In this paper, we prove that the Morley element eigenvalues approximate the exact ones from below on regular meshes, including adaptive local refined meshes, for the fourth-order e…
Error estimates and a two grid scheme for approximating transmission eigenvalues
Yidu Yang, Jiayu Han, Hai Bi
In this paper, using the linearization technique we write the Helmholtz transmission eigenvalue problem as an equivalent nonselfadjoint linear eigenvalue problem whose left-hand si…