Algorithm

Convection–diffusion equation

Smoothing

Statistics

Applied mathematics

Convergence (economics)

Numbering

Economics

Mathematical optimization

Dentistry

Grid

Thermodynamics

Physics

Calculus (dental)

Diffusion

Mathematics

Flow (mathematics)

Multigrid method

Mathematical analysis

Geometry

Medicine

Economic growth

Partial differential equation

Meteorology

Mechanics

Convection

Applied Numerical Mathematics

In the present paper, we introduce and investigate a robust smoothing strategy for convection-diffusion problems in two and three space dimensions without any assumption on the grid structure. The main tool to obtain such a robust smoother for these problems is an ordering strategy for the grid points called “downwind numbering” which follows the flow direction and, combined with a Gauss-Seidel type smoother, yields robust multigrid convergence for adaptively refined grids, provided the convection field is cycle-free. The algorithms are of optimum complexity and the corresponding smoothers are shown to be robust in numerical tests.

Downwind numbering: robust multigrid for convection-diffusion problems