Kopteva, Natalia; Stynes, Martin A robust adaptive method for a quasi-linear one-dimensional convection-diffusion problem. (English) Zbl 1012.65076 SIAM J. Numer. Anal. 39, No. 4, 1446-1467 (2001). A quasi-linear conservative convection-diffusion two-point boundary value problem is considered. The numerical solution involves an upwind finite difference scheme with a fixed number of nodes \(N\), in which the nodes are moved adaptively according to equidistribution of arc-length. It is proved that a mesh exists which equidistributes the arc-length along the polygonal solution curve interpolating the solution nodes, and that the solution is first order accurate uniformly in the diffusion coefficient. Numerical examples are given which support the theoretical results. Reviewer: Eugene L.Allgower (Fort Collins) Cited in 64 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 65L12 Finite difference and finite volume methods for ordinary differential equations 65L70 Error bounds for numerical methods for ordinary differential equations 65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:quasi-linear conservative convection-diffusion two-point boundary value problem; adaptive mesh; upwind finite difference scheme; numerical examples; error bounds PDFBibTeX XMLCite \textit{N. Kopteva} and \textit{M. Stynes}, SIAM J. Numer. Anal. 39, No. 4, 1446--1467 (2001; Zbl 1012.65076) Full Text: DOI