Perthame, B. Convergence of \(N\)-schemes for linear advection equations. (English) Zbl 0861.76071 Monteiro Marques, Manuel D. P. (ed.) et al., Trends in applications of mathematics to mechanics. A collection of selected papers presented at the 9th symposium, STAMM-94, held at Lisbon University, Lisbon, Portugal, July 1994. New York, NY: Longman. Pitman Monogr. Surv. Pure Appl. Math. 77, 323-333 (1995). The \(N\)-scheme (named after its Narrow stencil) is a numerical approximation to transport equations, which belongs to the class of fluctuation distribution schemes. In these schemes, a residual due to a flux balance is computed for each grid cell and then is distributed to the nodes of the grid according to certain distribution rules. Hence, the \(N\)-scheme is a genuinely multidimensional scheme. In the present paper the author is able to give a convergence proof concerning strong convergence in \(L^2\) of the \(N\)-scheme applied to a linear transport equation with constant coefficients. The main idea is the reformulation of the scheme as a finite volume scheme. Then the convergence can be proved by means of weak BV bounds.For the entire collection see [Zbl 0827.00054]. Reviewer: Th.Sonar (Hamburg) Cited in 1 Document MSC: 76M25 Other numerical methods (fluid mechanics) (MSC2010) 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs Keywords:\(L(2)\)-convergence; fluctuation distribution schemes; multidimensional scheme; constant coefficients; finite volume scheme; weak BV bounds PDFBibTeX XMLCite \textit{B. Perthame}, Pitman Monogr. Surv. Pure Appl. Math. 77, 323--333 (1995; Zbl 0861.76071)