In this paper we analyze the consistency, the accuracy and some entropy properties of
particle 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. I
343 (2006) 51–56] we re-write particle methods with remeshing in
the 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 Magni
devised recently in [G.-H. Cottet and A. Magni, C. R. Acad. Sci. Paris, Ser. I
347 (2009) 1367–1372] and [A. Magni and G.-H. Cottet, J.
Comput. Phys. 231 (2012) 152–172] TVD remeshing schemes for
particle methods. We extend these results to the nonlinear case with arbitrary velocity
sign. We present numerical results obtained with these new TVD particle methods for the
Euler equations in the case of the Sod shock tube. Then we prove that with these new TVD
remeshing schemes the particle methods converge toward the entropy solution of the scalar