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A fourth-order compact difference scheme on face centered cubic grids with multigrid method for solving 2D convection diffusion equation. (English) Zbl 1036.65082

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.

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:
65N06Finite difference methods (BVP of PDE)
35J25Second order elliptic equations, boundary value problems
65F10Iterative methods for linear systems
65N12Stability and convergence of numerical methods (BVP of PDE)
65N55Multigrid methods; domain decomposition (BVP of PDE)
65N15Error bounds (BVP of PDE)