214 | RWTH Publication No: 47168 2002   IGPM214pdf |
TITLE | On Fictitious Domain Formulations for Maxwell's Equations |
AUTHORS | Wolfgang Dahmen, Torben Klint, Karsten Urban |
ABSTRACT | We consider fictitious domain-Lagrange multiplier formulations for variational problems in the space H(curl; Ω) derived from Maxwell's equations. Boundary conditions and the divergence constraint are imposed weakly by using Lagrange multipliers. Both the time dependent and time harmonic formulations of the Maxwell's equations are considered, and we derive well-posed formulations for both cases. The arising variational problem can be discretized by functions that do not satisfy an a-priori divergence constraint. |
KEYWORDS | Maxwell's equations, fictitious domain method, saddle point problems, Lagrange multipliers |
DOI | 10.1007/s10208-002-0063-9 |
PUBLICATION | Foundations of computational mathematics 3(2), 135-160 (2003) |