On the application of lacunae-based methods to Maxwellʹs equations

A straightforward application of the previously designed lacunae-based numerical methods to unsteady electromagnetic problems would encounter certain difficulties, as it may violate the continuity of the charges and currents, which is a necessary solvability condition for the Maxwell equations. In the paper, we prove existence of the special auxiliary charges and currents that satisfy the continuity equations identically. We also show that using such charges and currents as a part of the numerical procedure provides a clear and unobstructed venue toward implementation of the lacunae-based methods in electromagnetics.