Abstract
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 l2 stability results and error estimates for the methods are proved. Numerical experiments confirm that these methods are one-sided l2 stable for convex flux instead of the usual Lip+ stability.
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