The convergence of the horizontal line method for Maxwell's equations

摘要

AbstractThe interior initial‐boundary value problem for Maxwell's equations is considered for certain homogeneous boundary conditions and currents which satisfy corresponding compatibility conditions. Under the assumption that a solution exists, it is shown by means of suitable normed spaces that the sequence of discrete solutions obtained from the horizontal line method converges discretely to this solution. A priori estimations are given both for the discrete solutions and the solution of the given proble