Liangkun Xu | Searcharxiv

arXiv2026

A high order stabilization-free virtual element method for general second-order elliptic eigenvalue problem

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.

math.NA↗

arXiv2025

A virtual element approximation for the modified transmission eigenvalues for natural materials

In this paper, we discuss a virtual element approximation for the modified transmission eigenvalue problem in inverse scattering for natural materials. In this case, due to the positive artificial diffusivity parameter in the considered problem, the sesquilinear form at the left end of the variational form is not coercive. We first demonstrate the well-posedness of the discrete source problem using the $\mathds{T}$-coercivity property, then provide the a priori error estimates for the approximate eigenspaces and eigenvalues, and finally report several numerical examples. The numerical experiments show that the proposed method is effective.

math.NA↗