R. Bruce Kellogg

Analysis of some difference approximations for a singular perturbation problem without turning points

Some three point difference schemes are considered for a singular perturbation problem without turning points. Bounds for the discretization error are obtained which are uniformly valid for all h and e > 0. The degeneration of the order of the schemes at e = 0 is considered.

Asymptotic anaylsis of a singular perturbation problem

We study, in a rectangle

A priori estimates and analysis of a numerical method for a turning point problem

0 < x < a

Compressible Navier-Stokes equations in a bounded domain with inflow boundary condition

and

Sharpened bounds for corner singularities and boundary layers in a simple convection–diffusion problem☆

0 < y < b

A Tailored Finite Point Method for a Singular Perturbation Problem on an Unbounded Domain

, the Dirichlet problem for an elliptic differential equation of the form \[ - \epsilon \Delta u\epsilon + p\frac{{\partial u\epsilon }}{{\partial x}} + qu\epsilon = f(x,y)\] where

A finite element method for the compressible Stokes equations

\epsilon

Finite element analysis of a scattering problem

is a small parameter

A finite difference method on layer-adapted meshes for an elliptic reaction-diffusion system in two dimensions

0 < \epsilon \ll 1

Regularity of solutions to the Navier-Stokes system for compressible flows on a polygon

,