Skip to main content
Log in

Uniform Pointwise Convergence of Finite Difference Schemes Using Grid Equidistribution

  • Published:
Computing Aims and scope Submit manuscript

Abstract

A singularly perturbed quasilinear two-point boundary value problem is considered. The problem is discretized using a simple upwind finite difference scheme on adapted meshes using grid equidistribution of monitor functions. We derive sufficient conditions on the monitor function that guarantee uniform convergence in the discrete maximum norm no matter how small the perturbation parameter is. These results can be used to deduce uniform convergence of the scheme for a number of layer-adapted meshes. We also propose an adaptive procedure for the numerical treatment of the boundary value problem. Numerical experiments for the schemes are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Additional information

Received November 12, 1999; revised April 20, 2000

Rights and permissions

Reprints and permissions

About this article

Cite this article

Linß, T. Uniform Pointwise Convergence of Finite Difference Schemes Using Grid Equidistribution. Computing 66, 27–39 (2001). https://doi.org/10.1007/s006070170037

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s006070170037

Navigation