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)