On a novel mesh for the regular boundary layers arising in advection‐dominated transport in two dimensions

Alan F. Hegarty, John J.H. Miller, Eugene O'riordan, G. I. Shishkin

Research output: Contribution to journalArticlepeer-review

Abstract

Upwind finite difference operators on uniform meshes are well known to be unsuitable for the numerical solution of singularly perturbed partial differential equations, in the sense that, in the neighbourhood of the boundary layers, the error in the numerical approximation may increase as the mesh is refined. Recently, on the other hand, it has been predicted theoretically that the use of upwind finite difference operators on specially designed piecewise uniform meshes guarantees the decrease of the nodal error to zero as the number of mesh elements increases. In the paper the general theorem is quoted and its prediction is validated by numerical experiment for a specific linear advection‐dominated transport equation in two dimensions. Experimental values of the convergence rate are obtained, which also agree with the theoretical estimates.

Original languageEnglish
Pages (from-to)435-441
Number of pages7
JournalCommunications in Numerical Methods in Engineering
Volume11
Issue number5
DOIs
Publication statusPublished - May 1995

Keywords

  • advection‐dominated transport
  • numerical experiments
  • piecewise uniform mesh
  • regular boundary layers
  • singular perturbations
  • ϵ‐uniform numerical method

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