An hp-version interior penalty discontinuous Galerkin method for the quad-curl eigenvalue problem
Abstract
An hp-version interior penalty discontinuous Galerkin (IPDG) method under nonconforming meshes is proposed to solve the quad-curl eigenvalue problem. We prove well-posedness of the numerical scheme for the quad-curl equation and then derive an error estimate in a mesh-dependent norm, which is optimal with respect to h but has different p-version error bounds under conforming and nonconforming tetrahedron meshes. The hp-version discrete compactness of the DG space is established for the convergence proof. The performance of the method is demonstrated by numerical experiments using conforming/nonconforming meshes and h-version/p-version refinement. The optimal h-version convergence rate and the exponential p-version convergence rate are observed.
Cite
@article{arxiv.2206.03764,
title = {An hp-version interior penalty discontinuous Galerkin method for the quad-curl eigenvalue problem},
author = {Jiayu Han and Zhimin Zhang},
journal= {arXiv preprint arXiv:2206.03764},
year = {2022}
}