A high order stabilization-free virtual element method for general second-order elliptic eigenvalue problem
It provides a novel numerical method for solving eigenvalue problems on complex polygonal meshes, improving accuracy and stability for computational scientists.
This paper develops a higher-order stabilization-free virtual element method for general second-order elliptic eigenvalue problems, achieving optimal error estimates for eigenspace and eigenvalues, validated on various polygonal meshes.
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 derived for both the approximate eigenspace and eigenvalues. Numerical experiments are conducted on regular convex polygonal meshes, convex-concave polygonal meshes, and concave polygonal meshes. The numerical results validate the effectiveness of the proposed method.