Convergence of fluctuation-splitting schemes for two dimensional scalar conservation laws with a kinetic solver

Summary. The “fluctuation-splitting schemes” (FSS in short) have been introduced by Roe and Sildikover to solve advection equations on rectangular grids and then extended to triangular grids by Roe, Deconinck, Struij... For a two dimensional nonlinear scalar conservation law, we consider the case of a triangular grid and of a kinetic approach to reduce the discretization of the nonlinear equation to a linear equation and apply a particular FSS called N-scheme. We show that the resulting scheme converges strongly in in a finite volume sense. Received February 25, 1997 / Revised version received November 8, 1999 / Published online August 24, 2000