# Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes

Loula Fezoui; Stéphane Lanteri; Stéphanie Lohrengel^{[1]}; Serge Piperno

- [1] Dieudonné Lab., UNSA, UMR CNRS 6621, Parc Valrose, 06108 Nice Cedex 2, France.

- Volume: 39, Issue: 6, page 1149-1176
- ISSN: 0764-583X

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topFezoui, Loula, et al. "Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.6 (2005): 1149-1176. <http://eudml.org/doc/244803>.

@article{Fezoui2005,

abstract = {A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved for metallic cavities. Convergence is proved for $\mathbb \{P\}_k$ Discontinuous elements on tetrahedral meshes, as well as a discrete divergence preservation property. Promising numerical examples with low-order elements show the potential of the method.},

affiliation = {Dieudonné Lab., UNSA, UMR CNRS 6621, Parc Valrose, 06108 Nice Cedex 2, France.},

author = {Fezoui, Loula, Lanteri, Stéphane, Lohrengel, Stéphanie, Piperno, Serge},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {electromagnetics; finite volume methods; discontinuous Galerkin methods; centered fluxes; leap-frog time scheme; $L^2$ stability; unstructured meshes; absorbing boundary condition; convergence; divergence preservation},

language = {eng},

number = {6},

pages = {1149-1176},

publisher = {EDP-Sciences},

title = {Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes},

url = {http://eudml.org/doc/244803},

volume = {39},

year = {2005},

}

TY - JOUR

AU - Fezoui, Loula

AU - Lanteri, Stéphane

AU - Lohrengel, Stéphanie

AU - Piperno, Serge

TI - Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2005

PB - EDP-Sciences

VL - 39

IS - 6

SP - 1149

EP - 1176

AB - A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved for metallic cavities. Convergence is proved for $\mathbb {P}_k$ Discontinuous elements on tetrahedral meshes, as well as a discrete divergence preservation property. Promising numerical examples with low-order elements show the potential of the method.

LA - eng

KW - electromagnetics; finite volume methods; discontinuous Galerkin methods; centered fluxes; leap-frog time scheme; $L^2$ stability; unstructured meshes; absorbing boundary condition; convergence; divergence preservation

UR - http://eudml.org/doc/244803

ER -

## References

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