L-2-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes

We investigate sufficient and possibly necessary conditions for the L-2 sta bility 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 thre e space dimensions. We show this condition is necessary for a class of regu lar meshes in two space dimensions. However, numerical tests show it is not necessary in three space dimensions even on regular meshes. Stability limi ts for time and space schemes with higher orders of accuracy are numericall y investigated.