A potential-based finite-element method for time-dependent Maxwell’s equations

Abstract

A fully discrete potential-based finite-element method which is called the A–φ approach is used to approximate time-dependent Maxwell’s equations in a three-dimensional bounded and convex domain. By appending the Coulomb gauge in the form of a penalty function to the magnetic vector potential, the existence and uniqueness of approximated solutions are ensured. Further, an optimal energy-norm error estimate is given and some computer simulation tests are performed to demonstrate the validity of our schemes.

Keywords:

• Maxwell’s equations
• A–φ
• approach
• Nodal element
• Error estimate

Acknowledgements

This work was supported by Com²MaC-KOSEF, Postech BSRI research fund 2004 and the scientific research fund of the State Administration of Radio, Film and TV of China.