A hybridizable discontinuous Galerkin method for the quad-curl problem
This work provides a numerical method for solving quad-curl problems in electromagnetics and magnetohydrodynamics, but the results are theoretical without concrete numerical experiments or comparisons.
The paper develops a hybridizable discontinuous Galerkin method for the quad-curl problem, enforcing divergence-free conditions via a Lagrange multiplier, and provides analysis for low-regularity solutions on Lipschitz polyhedron domains.
The quad-curl problem arises in magnetohydrodynamics, inverse electromagnetic scattering and transform eigenvalue problems. In this paper we investigate a hybridizable discontinuous Galerkin method to solve the quad-curl problem based on a mixed formulation. The divergence-free condition is enforced by introducing a Lagrange multiplier into the system. The analysis is performed for the model problem with low regularity, which is posed on a Lipschitz polyhedron domain.