### Abstract

We consider fictitious domain-Lagrange multiplier formulations for variational problems in the space H(curl: Omega) 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 variational problem that arises can be discretized by functions that do not satisfy an a-priori divergence constraint.

Original language | English |
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Journal | Foundations of computational mathematics |

Volume | 3 |

Issue number | 2 |

Pages (from-to) | 135-160 |

ISSN | 1615-3375 |

Publication status | Published - 2003 |

## Cite this

Dahmen, W., Jensen, T. K., & Urban, K. (2003). On fictitious domain formulations for Maxwell's equations.

*Foundations of computational mathematics*,*3*(2), 135-160.