On fictitious domain formulations for Maxwell's equations

W. Dahmen, Torben Klint Jensen, K. Urban

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    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 languageEnglish
    JournalFoundations of computational mathematics
    Volume3
    Issue number2
    Pages (from-to)135-160
    ISSN1615-3375
    Publication statusPublished - 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.