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N -widths for singularly perturbed problems

Martin Stynes;  R. Bruce Kellogg — 2002

Mathematica Bohemica

Kolmogorov N -widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the N -widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.

Origins, analysis, numerical analysis, and numerical approximation of a forward-backward parabolic problem

A. Kadir Aziz;  Donald A. French;  Soren Jensen;  R. Bruce Kellogg — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the analysis and numerical solution of a forward-backward boundary value problem. We provide some motivation, prove existence and uniqueness in a function class especially geared to the problem at hand, provide various energy estimates, prove error estimates for the Galerkin method, and show the results of some numerical computations.

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