Estimates for Deviations from Exact Solutions of Maxwell's Initial   Boundary Value Problem
  In this paper, we consider an initial boundary value problem for Maxwell's equations. For this hyperbolic type problem, we derive guaranteed and computable upper bounds for the difference between the exact solution and any pair of vector fields in the space-time cylinder that belongs to the corresponding admissible energy class. For this purpose, we use a method suggested earlier for the wave equation. 
Dirk Pauly, Sergey Repin, Tuomo Rossi
math.AP math-ph math.MP math.NA