A robust layer-resolving spline collocation method for a convection-diffusion problem
This paper deals with the singularly perturbed convection-diffusion model problem \[ \varepsilon y''+ a(x) y'- b(x) y= f(x),\;x\in (0,1),\;y(0)= \gamma_0,\;y(1)= \gamma_1,\;0<\varepsilon\ll 1. \] Presented numerical method is based on a difference scheme which is obtained by: a) quadratic spline function as an approximation function in the collocation process, b) Layer-adepted Shishkin mesh. The collocation points are moved in order to obtain the validity of the discrete minimum principle which enables application of the barrier function technique. Some convergence results are presented.
scientific article; zbMATH DE number 5522159