In this paper we analyze the consistency, the accuracy and some entropy properties ofparticle methods with remeshing in the case of a scalar one-dimensional conservation law.As in [G.-H. Cottet and L. Weynans, C. R. Acad. Sci. Paris, Ser. I343 (2006) 51–56] we re-write particle methods with remeshing inthe finite-difference formalism. This allows us to prove the consistency of these methods,and accuracy properties related to the accuracy of interpolation kernels. Cottet and Magnidevised recently in [G.-H. Cottet and A. Magni, C. R. Acad. Sci. Paris, Ser. I347 (2009) 1367–1372] and [A. Magni and G.-H. Cottet, J.Comput. Phys. 231 (2012) 152–172] TVD remeshing schemes forparticle methods. We extend these results to the nonlinear case with arbitrary velocitysign. We present numerical results obtained with these new TVD particle methods for theEuler equations in the case of the Sod shock tube. Then we prove that with these new TVDremeshing schemes the particle methods converge toward the entropy solution of the scalarconservation law.
