TY - JOUR
T1 - On a novel mesh for the regular boundary layers arising in advection‐dominated transport in two dimensions
AU - Hegarty, Alan F.
AU - Miller, John J.H.
AU - O'riordan, Eugene
AU - Shishkin, G. I.
PY - 1995/5
Y1 - 1995/5
N2 - 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.
AB - 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.
KW - advection‐dominated transport
KW - numerical experiments
KW - piecewise uniform mesh
KW - regular boundary layers
KW - singular perturbations
KW - ϵ‐uniform numerical method
UR - http://www.scopus.com/inward/record.url?scp=0029412208&partnerID=8YFLogxK
U2 - 10.1002/cnm.1640110508
DO - 10.1002/cnm.1640110508
M3 - Article
AN - SCOPUS:0029412208
SN - 1069-8299
VL - 11
SP - 435
EP - 441
JO - Communications in Numerical Methods in Engineering
JF - Communications in Numerical Methods in Engineering
IS - 5
ER -