Analysis of the upwind finite volume method for general initial- and boundary-value transport problems

@article{Boyer2012AnalysisOT,
  title={Analysis of the upwind finite volume method for general initial- and boundary-value transport problems},
  author={Franck Boyer},
  journal={Ima Journal of Numerical Analysis},
  year={2012},
  volume={32},
  pages={1404-1439}
}
  • F. Boyer
  • Published 1 October 2012
  • Mathematics
  • Ima Journal of Numerical Analysis
This paper is devoted to the convergence analysis of the upwind finite volume scheme for the initial and boundary value problem associated to the linear transport equation in any dimension, on general unstructured meshes. We are particularly interested in the case where the initial and boundary data are in $L^\infty$ and the advection vector field $v$ has low regularity properties, namely $v\in L^1(]0,T[,(W^{1,1}(\O))^d)$, with suitable assumptions on its divergence. In this general framework… 

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