Two-grid discretizations and a local finite element scheme for a non-selfadjoint Stekloff eigenvalue problem
Provides numerical methods for a challenging eigenvalue problem in computational mathematics, but the contribution is incremental as it extends existing two-grid techniques to a new problem class.
The paper develops two-grid discretization and local finite element schemes for a non-selfadjoint Stekloff eigenvalue problem, providing error estimates and numerical validation of efficiency.
In this paper, for a new Stekloff eigenvalue problem which is non-selfadjoint and not $H^1$-elliptic, we establish and analyze two kinds of two-grid discretization scheme and a local finite element scheme. We present the error estimates of approximations of two-grid discretizations. We also prove a local error estimate which is suitable for the case that the local refined region contains singular points lying on the boundary of domain. Numerical experiments are reported finally to show the efficiency of our schemes.