TY - JOUR
T1 - Uniformly convergent multigrid methods for convection-diffusion problems without any constraint on coarse grids
AU - Kim, Hwanho
AU - Xu, Jinchao
AU - Zikatanov, Ludmil
PY - 2004/5/1
Y1 - 2004/5/1
N2 - We construct a class of multigrid methods for convection-diffusion problems. The proposed algorithms use first order stable monotone schemes to precondition the second order standard Galerkin finite element discretization. To speed up the solution process of the lower order schemes, cross-wind-block reordering of the unknowns is applied. A V-cycle iteration, based on these algorithms, is then used as a preconditioner in GMRES. The numerical examples show that this method is convergent without imposing any constraint on the coarsest grid and the convergence of the preconditioned method is uniform.
AB - We construct a class of multigrid methods for convection-diffusion problems. The proposed algorithms use first order stable monotone schemes to precondition the second order standard Galerkin finite element discretization. To speed up the solution process of the lower order schemes, cross-wind-block reordering of the unknowns is applied. A V-cycle iteration, based on these algorithms, is then used as a preconditioner in GMRES. The numerical examples show that this method is convergent without imposing any constraint on the coarsest grid and the convergence of the preconditioned method is uniform.
UR - http://www.scopus.com/inward/record.url?scp=4043129615&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=4043129615&partnerID=8YFLogxK
U2 - 10.1023/A:1027378015262
DO - 10.1023/A:1027378015262
M3 - Article
AN - SCOPUS:4043129615
VL - 20
SP - 385
EP - 399
JO - Advances in Computational Mathematics
JF - Advances in Computational Mathematics
SN - 1019-7168
IS - 4
ER -