Space–time variational methods for Maxwell's equations

The efficient and accurate numerical solution of the time–dependent Maxwell equations is one of the most challenging tasks, see, e.g., [1]. Besides semi–discretization methods such as the method of lines and Laplace transformation approaches, space–time variational formulations became popular in recent years. Here the variational principle is applied simultaneously in space and time, which later requires the solution of the global linear system of algebraic equations. But this can be done in parallel, and the space–time formulation allows for an adaptive resolution of the solution in space and time simultaneously. Following previous work [3,5] on the acoustic wave equation we present two variational formulations for the solution of the electromagnetic wave equation.