ISSN:
1069-8299
Keywords:
regular boundary layers
;
∊-uniform numerical method
;
advection-dominated transport
;
piecewise uniform mesh
;
singular perturbations
;
numerical experiments
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
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.
Additional Material:
3 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/cnm.1640110508
