Benítez, MartaChacón Rebollo, TomásGómez Mármol, María MacarenaNarbona-Reina, Gladys2024-02-072024-02-072011-01-01Benítez García, M., Chacón Rebollo, T., Gómez Mármol, M., Narbona-Reina, G. (2011). Numerical Approximation of Convection-Diffusion Problems Through the PSI Method and Characteristics Method. In: C. Clavero, J. Gracia, F. Lisbona (eds.) BAIL 2010 - Boundary and Interior Layers, Computational and Asymptotic Methods. Lecture Notes in Computational Science and Engineering, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19665-2_31439-73582197-7100 (e-ISSN)http://hdl.handle.net/2183/35479This version of the chapter has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/978-3-642-19665-2_3[Abstract]: In this work we present some numerical methods for solving evolutive convection-diffusion problems. In order to obtain a physically admissible solution we search for monotone and accurate methods that are also non-linear due to the Godunov’s theorem. We will center in Fluctuation Splitting methods, [8], in particular in PSI scheme, and characteristic type methods, where a new Lagrangian method is proposed. Finally, a numerical test is presented to assess the performance of the numerical methods described in the present work.eng© Springer-Verlag Berlin Heidelberg 2011Convection-diffusion equationCharacteristics methodFluctuation spliting schemesGalerkin discretizationbook partopen accesshttps://doi.org/10.1007/978-3-642-19665-2_3