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A robust adaptive method for a quasi-linear one-dimensional convection-diffusion problem. (English) Zbl 1012.65076
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.

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
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