Natalia Kopteva

A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem

A quasi-linear conservative convection-diffusion two-point boundary value problem is considered. To solve it numerically, an upwind finite difference scheme is applied. The mesh used has a fixed number (N+1) of nodes and is initially uniform, but its nodes are moved adaptively using a simple algorithm of de Boor based on equidistribution of the arc-length of the current computed piecewise linear solution. It is proved for the first time that a mesh exists that equidistributes the arc-length along the polygonal solution curve and that the corresponding computed solution is first-order accurate, uniformly in

Maximum Norm A Posteriori Error Estimates for a One-Dimensional Convection-Diffusion Problem

\varepsilon

The Formation of River Channels

, where

Steady rimming flows with surface tension

\varepsilon

Approximation of derivatives in a convection-diffusion two-point boundary value problem

is the diffusion coefficient. In the case when the boundary value problem is linear, if N is sufficiently large independently of

Maximum Norm A Posteriori Error Estimate for a 2D Singularly Perturbed Semilinear Reaction-Diffusion Problem

\varepsilon

Grid equidistribution for reaction–diffusion problems in one dimension

, it is shown that after

Uniform second-order pointwise convergence of a central difference approximation for a quasilinear convection-diffusion problem

O({\rm ln}(1/\varepsilon)/{\rm ln} N)

Error Expansion for an Upwind Scheme Applied to a Two-Dimensional Convection-Diffusion Problem

iterations of the algorithm, the piecewise linear interpolant of the computed solution achieves first-order accuracy in the

Maximum Norm A Posteriori Error Estimation for Parabolic Problems Using Elliptic Reconstructions

L^\infty[0,1]