Convergence of a Discontinuous Galerkin scheme for the mixed time domain Maxwell's equations in dispersive media.

Stephane Lanteri (1) , Claire Scheid (1, 2)

1 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media
2 LJAD - Laboratoire Jean Alexandre Dieudonné

This work is about the numerical solution of the time-domain Maxwell's equations in dispersive propagation media by a discontinuous Galerkin time-domain method. The Debye model is used to describe the dispersive behaviour of the media. The resulting system of differential equations is solved using a centred-flux discontinuous Galerkin formulation for the discretization in space and a second-order leapfrog scheme for the integration in time. The numerical treatment of the dispersive model relies on an auxiliary differential equation approach similar to that which is adopted in the finite difference time-domain method. Stability estimates are derived through energy considerations and convergence is proved for both the semidiscrete and the fully discrete schemes.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Stephane Lanteri, Claire Scheid. Convergence of a Discontinuous Galerkin scheme for the mixed time domain Maxwell's equations in dispersive media.. IMA Journal of Numerical Analysis, 2013, 33 (2), pp.432-459. ⟨10.1093/imanum/drs008⟩. ⟨hal-00874752⟩