On Convergence of Minmod-Type Schemes
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A class of nonoscillatory numerical methods for solving nonlinear scalar conservation laws in one space dimension is considered. This class of methods contains the classical Lax-Friedrichs and the second-order Nessyahu-Tadmor schemes. In the case of linear flux, new l 2 stability results and error estimates for the methods are proved. Numerical experiments confirm that these methods are one-sided l 2 stable for convex flux instead of the usual Lip+ stability. © 2005 Society for Industrial and Applied Mathematics.
author list (cited authors)
Konyagin, S., Popov, B., & Trifonov, O.