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IGPM223.pdf November 2002 
TITLE 
Convergence Analysis of a Multigrid Solver for a Finite Element Method Applied to ConvectionDiffusion Problems 
AUTHORS 
Maxim A. Olshanskii, Arnold Reusken 
ABSTRACT 
The paper presents a convergence analysis of a multigrid solver for a system of
linear algebraic equations resulting from the disretization of a convectiondiffusion problem using a finite element method. We consider piecewise linear finite elements in combination with a streamline diffusion stabilization. We analyze a multigrid method that is based on canonical intergrid transfer operators, a "direct discretization" approach for the coarsegrid operators, a smoother of lineJacobi
type and one nonstandard component which is called a "local presolver". A robust (diffusion and hindependent) bound for the contraction number of the twogrid method and the multigrid Wcycle are proved for a special class of convectiondiffusion problems, namely with Neumann conditions on the out boundary, Dirichlet conditions on the rest of the boundary and a direction that is constant and aligned with gridlines. Our convergence analysis is based on modified smoothing and
approximation properties. The arithmetic complexity of one multigrid iteration is optimal up to a logarithmic term.

KEYWORDS 
multigrid, streamline diffusion, convectiondiffusion 