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Journals and Conferences
This paper deals with the upwind finite volume method applied to the linear advection equation on a bounded domain and with natural boundary conditions. We introduce what we call the geometric corrector which is a sequence associated with every finite volume mesh in Rnd and every non vanishing vector a of Rnd. First we show that if the continuous solution… (More)
An asymptotic formula for the problem of diffraction by a strongly elongated body of revolution is constructed. Its uniform nature with respect to the parameter that characterizes the rate of elongation is demonstrated. The results are in good agreement with numerical simulations.
In this paper we study the error estimate of the upwind first order finite volume scheme applied to scalar conservation laws. As a first step we also consider the case of a linear equation with space variable coefficients in conservation form. We prove that indeed these schemes lead to a first order error estimate. This work follows our previous paper … (More)
On considbre le problbme de la diffraction d'une onde glectromagn~tique par une perturbation locale des caractdristiques d'un rev~tement (ou inclusion). L'inclusion induit un champ diffractS, que l' on ddfinit comme la diffdrence entre le champ diffract( par l'objet avec inclusion et le champ diffractd par l'objet sans inclusion. On montre que le champ… (More)
The problem of high-frequency diffraction by a strongly elongated body is considered. The surface is supposed to be well approximated by a spheroidal surface. The asymptotic approximation for the induced currents is constructed by means of the parabolic equation method under the assumption that the wave-size of the body in the longitudinal direction is of… (More)
This paper provides a survey of solution methods and diffraction coefficients for curvature and higher order discontinuities.