Numerical Methods for Conservation Laws: From Analysis to Algorithms

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A robust optimization approach for dynamic traffic signal control with emission considerations (2012, methodology): “For a detailed discussion of numerical schemes for conservation laws, we refer the reader to Godunov (1959) and LeVeque (1992).”
Modeling Sea Ice Transport Using Incremental Remapping (2004, methodology): “There are many numerical methods for solving transport equations ( LeVeque 1992 ).”
An adaptive discretization of shallow‐water equations based on discontinuous Galerkin methods (2006, background): “For non linear problems, it has been proven that the choice of Godunov uxes are ensuring that the numerical solution satis es the entropy condition [13].”
Numerical simulations of transportational cyclic steps (2003, methodology): “This discussion is the extension of the theory of shock waves in shallow waters (easily found in Stoker, 1957; LeVeque, 1992) to the new system of equations.”
Sap flow and sugar transport in plants (2016, methodology): “Well known in gas theory, this gives a simple approximative way of handling shocks (LeVeque, 1992) and it works well for the Münch-Horwitz equations (see the discussion of the target concentration models in Sec.”