===affil2:
Lawrence Technological University
===firstname:
Christopher
===firstname4:
Jun
===firstname3:
Ruxin
===lastname2:
Wang
===lastname:
Kawatsu
===firstname5:

===affil6:

===lastname3:
Dai
===email:
ckawatsu@ltu.edu
===lastname6:

===affil5:

===otherauths:

===lastname4:
Zhang
===affil4:
University of Kentucky
===lastname7:

===affil7:

===firstname7:

===postal:
Department of Mathematics and Computer Science, Lawrence Technological University, 21000 West Ten Mile Road,
Southfield, MI, 48075-1058
===firstname6:

===ABSTRACT:
A geometric multigrid method for solving the convection diffusion equation with boundary layers to sixth order accuracy is presented. A nine point finite difference discretization scheme is used to obtain fourth order accurate solutions on a coarse and a fine grid. Richardson extrapolation is used to increase the order of accuracy to sixth order on the coarse. An iterative smoothing technique is then used to obtain a sixth order solution on the fine grid. The discretization we used allows the grid to be a graded mesh. This is the first time the post extrapolation smoothing technique has been applied to a graded mesh. Numerical results are presented to demonstrate the use of a graded mesh can significantly decrease the maximum error compared to a regular mesh.
===affil3:
University of Kentucky
===lastname5:

===affilother:

===title:
A Sixth Order Compact Multigrid Solver for the Convection Diffusion Equation with Boundary Layers
===firstname2:
Yin