Divergence boundary conditions for vector Helmholtz equations with divergence constraints
Department of Mathematics, Tartu University, Tartu, Estonia.
2 Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA. The work of this author was supported by the United States Air Force Office of Scientific Research under grants F-49620-94-1-0311 and F-49620-97-1-0204.
The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.
Mathematics Subject Classification: 35L05 / 65N12 / 65M17
Key words: Maxwell's equations / divergence boundary conditions / Helmholtz equation / divergence constraints.
© EDP Sciences, SMAI, 1999