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Approximation of viscous transport and conservative equations with one sided Lipschitz velocity fields (2505.08970v1)
Published 13 May 2025 in math.NA and cs.NA
Abstract: The aim of this work is to investigate semi-Lagrangian approximation schemes on unstructured grids for viscous transport and conservative equations with measurable coefficients that satisfy a one-sided Lipschitz condition. To establish the convergence of the schemes, we exploit the characterization of the solution for these equations expressed in terms of measurable time-dependent viscosity solution and, respectively, duality solution. We supplement our theoretical analysis with various numerical examples to illustrate the features of the schemes.
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