L2-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes

Serge Piperno

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 1, page 139-158
  • ISSN: 0764-583X

Abstract

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We investigate sufficient and possibly necessary conditions for the L2 stability of the upwind first order finite volume scheme for Maxwell equations, with metallic and absorbing boundary conditions. We yield a very general sufficient condition, valid for any finite volume partition in two and three space dimensions. We show this condition is necessary for a class of regular meshes in two space dimensions. However, numerical tests show it is not necessary in three space dimensions even on regular meshes. Stability limits for time and space schemes with higher orders of accuracy are numerically investigated.

How to cite

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Piperno, Serge. "L2-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes." ESAIM: Mathematical Modelling and Numerical Analysis 34.1 (2010): 139-158. <http://eudml.org/doc/197507>.

@article{Piperno2010,
abstract = { We investigate sufficient and possibly necessary conditions for the L2 stability of the upwind first order finite volume scheme for Maxwell equations, with metallic and absorbing boundary conditions. We yield a very general sufficient condition, valid for any finite volume partition in two and three space dimensions. We show this condition is necessary for a class of regular meshes in two space dimensions. However, numerical tests show it is not necessary in three space dimensions even on regular meshes. Stability limits for time and space schemes with higher orders of accuracy are numerically investigated. },
author = {Piperno, Serge},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Electromagnetism; finite volume methods; L2 stability; energy methods; unstructured meshes; absorbing boundary condition; metallic boundary condition.; stability; finite volume scheme; Maxwell's equations; absorbing boundary conditions},
language = {eng},
month = {3},
number = {1},
pages = {139-158},
publisher = {EDP Sciences},
title = {L2-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes},
url = {http://eudml.org/doc/197507},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Piperno, Serge
TI - L2-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 1
SP - 139
EP - 158
AB - We investigate sufficient and possibly necessary conditions for the L2 stability of the upwind first order finite volume scheme for Maxwell equations, with metallic and absorbing boundary conditions. We yield a very general sufficient condition, valid for any finite volume partition in two and three space dimensions. We show this condition is necessary for a class of regular meshes in two space dimensions. However, numerical tests show it is not necessary in three space dimensions even on regular meshes. Stability limits for time and space schemes with higher orders of accuracy are numerically investigated.
LA - eng
KW - Electromagnetism; finite volume methods; L2 stability; energy methods; unstructured meshes; absorbing boundary condition; metallic boundary condition.; stability; finite volume scheme; Maxwell's equations; absorbing boundary conditions
UR - http://eudml.org/doc/197507
ER -

References

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