We compare the results obtained by applying the standard collocation method at the Legendre Gauss-Lobatto nodes, for a model problem simulating a steady advection-diffusion equation, with those obtained by collocating at a new set of nodes. These nodes are derived from a suitable modification of the Legendre grid, according to the magnitude of the ratio between the advective and the diffusive parts of the differential operator.
Some remarks about the collocation method on a modified Legendre grid / Funaro, Daniele. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - STAMPA. - 33:(1997), pp. 95-103.
Some remarks about the collocation method on a modified Legendre grid
FUNARO, Daniele
1997
Abstract
We compare the results obtained by applying the standard collocation method at the Legendre Gauss-Lobatto nodes, for a model problem simulating a steady advection-diffusion equation, with those obtained by collocating at a new set of nodes. These nodes are derived from a suitable modification of the Legendre grid, according to the magnitude of the ratio between the advective and the diffusive parts of the differential operator.
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