We introduce finite-difference schemes based on a special upwind-type collocation grid, in order to obtain approximations of the solution of linear transport-dominated advection-diffusion problems. The method is well suited when the diffusion parameter is very small compared to the discretization parameter. A theory is developed and many numerical experiments are shown.
Finite-difference schemes for transport-dominated equations using special collocation nodes / Fatone, Lorella; Funaro, Daniele; R., Giova. - In: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0749-159X. - STAMPA. - 21:4(2005), pp. 649-671. [10.1002/num.20056]
Finite-difference schemes for transport-dominated equations using special collocation nodes
FATONE, Lorella;FUNARO, Daniele;
2005
Abstract
We introduce finite-difference schemes based on a special upwind-type collocation grid, in order to obtain approximations of the solution of linear transport-dominated advection-diffusion problems. The method is well suited when the diffusion parameter is very small compared to the discretization parameter. A theory is developed and many numerical experiments are shown.
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