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

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.