An hp-version interior penalty discontinuous Galerkin method for the quad-curl eigenvalue problem

被引：0
作者：
Jiayu Han
Zhimin Zhang
机构：
[1] Guizhou Normal University,School of Mathematical Sciences
[2] Wayne State University,Department of Mathematics
来源：
BIT Numerical Mathematics | 2023年 / 63卷
关键词：
discontinuous Galerkin method; Quad-curl eigenvalue problem; Error estimate; Discrete compactness; 65N25; 65N30; 35Q60; 35B45;
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学科分类号：
摘要：
An hp-version interior penalty discontinuous Galerkin 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.
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