Abstract
This work is devoted to the convergence analysis of the implicit 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 concerned with the case where the initial and boundary data are in L ∞ and the advection vector field v has low regularity properties, namely v ∈ L 1(]0, T[, (W 1, 1(Ω))d), with suitable assumptions on its divergence. We prove strong convergence in L ∞(]0, T[, L p(Ω)) with p < + ∞, of the approximate solution towards the unique weak solution of the problem as well as the strong convergence of its trace.
Keywords
MSC2010: 35D30, 35L04, 65M08, 65M12
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Acknowledgements
The author wishes to thank T. Gallouët and R. Herbin for many stimulating discussions on the topic of this work.
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Boyer, F. (2011). Convergence Analysis of the Upwind Finite Volume Scheme for General Transport Problems. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_17
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DOI: https://doi.org/10.1007/978-3-642-20671-9_17
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