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L 2-stability of the upwind first order finite volume schemefor the Maxwell equations in two and three dimensionson arbitrary unstructured meshes

Published online by Cambridge University Press:  15 April 2002

Serge Piperno
Serge Piperno*
Affiliation:
CERMICS, INRIA, B.P. 93, 06902 Sophia-Antipolis Cedex, France. (Serge.Piperno@sophia.inria.fr)
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Abstract

We investigate sufficient and possiblynecessary conditions for the L 2 stability of the upwind first orderfinite volume scheme for Maxwell equations, with metallic andabsorbing boundary conditions. We yield a very general sufficient condition,valid for any finite volume partition in two and three spacedimensions. We show this condition is necessary for a class ofregular meshes in two space dimensions. However, numerical tests show it is not necessaryin three space dimensions even on regular meshes. Stability limits for time and space schemes with higher orders of accuracy are numericallyinvestigated.

Keywords

Electromagnetismfinite volume methodsL 2stabilityenergy methodsunstructured meshesabsorbing boundaryconditionmetallic boundary condition.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 1 , January 2000 , pp. 139 - 158
Copyright
© EDP Sciences, SMAI, 2000

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