High-order time-accurate schemes for parabolic singular perturbation problems with convection
We consider the first boundary value problem for a singularly perturbed para-bo-lic PDE with convection on an interval. For the case of sufficiently smooth data, it is easy to construct a standard finite difference operator and a piecewise uniform mesh, condensing in the boundary layer, which gives an $epsilon$-uniformly convergent difference scheme. The order of convergence for such a scheme is exactly one and up to a small logarithmic factor one with respect to the time and space variables, respectively. In this paper we construct high-order time-accurate $epsilon$-uniformly convergent schemes by a defect correction technique. The efficiency of the new defect-correction scheme is confirmed by numerical experiments.
|Finite difference methods (msc 65M06), Stability and convergence of numerical methods (msc 65M12), Error bounds (msc 65M15)|
|Life Sciences (theme 5), Energy (theme 4)|
|Modelling, Analysis and Simulation [MAS]|
Hemker, P.W, Shishkin, G.I, & Shishkina, L.P. (2001). High-order time-accurate schemes for parabolic singular perturbation problems with convection. Modelling, Analysis and Simulation [MAS]. CWI.