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l 2stability

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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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
Serge Piperno
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 34 / Issue 1 / January 2000

Published online by Cambridge University Press:

15 April 2002, pp. 139-158

Print publication:

January 2000
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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.