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Zbl 1036.65082
Sun, Haiwei; Kang, Ning; Zhang, Jun; Carlson, Eric S.
A fourth-order compact difference scheme on face centered cubic grids with multigrid method for solving 2D convection diffusion equation. (English)
[J] Math. Comput. Simul. 63, No. 6, 651-661 (2003). ISSN 0378-4754

Summary: We present a fourth-order compact finite difference scheme on the face centered cubic grids for the numerical solution of the two-dimensional convection diffusion equation. The seven-point formula is defined on a regular hexagon, where the strategy of directional derivative is employed to make the derivation procedure straightforward, efficient, and concise. A corresponding multigrid method is developed to solve the resulting sparse linear system. \par Numerical experiments are conducted to verify the fourth-order convergence rate of the derived discretization scheme and to show that the fourth-order compact difference scheme is computationally more efficient than the standard second-order central difference scheme.

MSC 2000:: *65N06 Finite difference methods (BVP of PDE)
35J25 Second order elliptic equations, boundary value problems
65F10 Iterative methods for linear systems
65N12 Stability and convergence of numerical methods (BVP of PDE)
65N55 Multigrid methods; domain decomposition (BVP of PDE)
65N15 Error bounds (BVP of PDE)

Keywords: Convection diffusion equation; Multigrid method; Face centered cubic grid; Fourth-order compact finite difference scheme; numerical examples; numerical experiments; convergence

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