Continuous Galerkin methods for solving the time-dependent Maxwell equations in 3D geometries

• Published in: Journal of computational physics Vol. 226; no. 1; pp. 1122 - 1135
• Main Authors: Ciarlet, Patrick, Jamelot, Erell
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 10-09-2007; Elsevier
• Subjects: 3D computations; Computational techniques; Exact sciences and technology; Mathematical methods in physics; Mathematics; Maxwell’s equations; Numerical Analysis; Numerical methods; Physics; Singular electromagnetic fields; 3D computations; Singular electromagnetic fields; Numerical methods; Maxwell’s equations; Galerkin-Petrov method; Divergences; Discretization; Numerical method; Calculation; Maxwell's equations; Electromagnetic fields; Maxwell equations; Calculation methods
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2007.05.029

A few years ago, Costabel and Dauge proposed a variational setting, which allows one to solve numerically the time-harmonic Maxwell equations in 3D geometries with the help of a continuous approximation of the electromagnetic field. In this paper, we investigate how their framework can be adapted to compute the solution to the time-dependent Maxwell equations. In addition, we propose some extensions, such as the introduction of a mixed variational setting and its discretization, to handle the constraint on the divergence of the field.