A Comparison of Three Mixed Methods for the Time-Dependent Maxwell's Equations

Three mixed finite-element methods for approximating Maxwell’s equations are compared. A dispersion analysis provides a Courant–Friedrichs–Lewy (CFL) bound that is necessary for convergence when a uniform mesh is used. The dispersion analysis also allows a comparison of the stability properties of the methods. Superconvergence at the interpolation points is proved for uniform grids, and demonstrated by three numerical examples. All three methods are shown to be able to handle discontinuous media without modification of the finite-element spaces. Since all three methods have three-dimensional counterparts, this study suggests that all three methods could be the basis of a successful three-dimensional code.

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