Convergence Rates for Upwind Schemes with Rough Coefficients

@article{Schlichting2017ConvergenceRF,
  title={Convergence Rates for Upwind Schemes with Rough Coefficients},
  author={Andr{\'e} Schlichting and Christian Seis},
  journal={SIAM J. Numer. Anal.},
  year={2017},
  volume={55},
  pages={812-840}
}
This paper is concerned with the numerical analysis of the explicit upwind finite volume scheme for numerically solving continuity equations. We are interested in the case where the advecting velocity field has spatial Sobolev regularity and initial data are merely integrable. We estimate the error between approximate solutions constructed by the upwind scheme and distributional solutions of the continuous problem in a Kantorovich--Rubinstein distance, which was recently used for stability… 

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