On Fictitious Domain Formulations for Maxwell's Equations |
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| Authors: | Wolfgang Dahmen Torben Klint Karsten Urban |
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| Affiliation: | (1) RWTH Aachen Institut für Geometrie und Praktische Mathematik Templergraben 55 D-52056 Aachen, Germany dahmen@igpm.rwth-aachen.de, DE;(2) Technical University of Denmark Department of Mathematics Matematiktorvet DK-2800 Lyngby, Denmark t.klint@mat.dtu.dk, DK;(3) University of Ulm Division of Numerics D-89069 Ulm, Germany kurban@mathematik.uni-ulm.de, DE |
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| Abstract: | We consider fictitious domain-Lagrange multiplier formulations for variational problems in the space H(curl: Ω{bf)} 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. |
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| Keywords: | . Maxwell's equations Fictitious domain method Saddle point problems Lagrange multipliers. AMS Classification. 35Q60 78A25 65J10 65N99 47F05. |
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