Naslov
Basis of splines associated with singularly perturbed advection–diffusion problems

Autori
Bosner, Tina

Izvornik
Mathematical communications (1331-0623) 15 (2010), 1; 1-12

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Singular perturbations ; advection–diffusion ; Chebyshev theory ; exponential tension splines ; knot insertion

Sažetak
Among fitted-operator methods for solving one-dimensional singular perturbation problems one of the most accurate is the collocation by linear combinations of{; ; ; ; 1, x, exp (±px)}; ; ; ; , known as tension spline collocation. There exist well established results for determining the ‘tension parameter’ p, as well as special collocation points, that provide higher order local and global convergence rates. However, if the advection–diffusion–reaction problem is specified in such a way that two boundary internal layers exist, the method is incapable of capturing only one boundary layer, which happens when no reaction term is present. For pure advection-diffusion problem we therefore modify the basis accordingly, including only one exponential, i.e. project the solution to the space locally spanned by {; ; ; ; 1, x, x^2, exp (px)}; ; ; ; where p > 0 is the tension parameter. The aim of the paper is to show that in this situation it is still possible to construct a basis of C1-locally supported functions by a simple knot insertion technique, commonly used in computer aided geometric design. We end by showing that special collocation points can be found, which yield better local and global convergence rates, similar to the tension spline case.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA