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Analysis of a fourth-order scheme for a three-dimensional convection-diffusion model problem. (English) Zbl 1128.65091
From the abstract: We derive closed form expressions for the eigenvalues and discrete solution arising from a 19-point compact discretization of a three-dimensional convection-diffusion problem. It is shown that the coefficient matrix is positive definite when the cell-Reynolds number is greater than some critical value. By analyzing the terms composing the discrete solution, we prove that an oscillation-free discrete solution is guaranteed whenever the cell-Reynolds number exceeds a value which is grid-size dependent. An interesting results is that as the mesh size is refined, this value approaches the golden mean.
MSC:
65N06Finite difference methods (BVP of PDE)
35J25Second order elliptic equations, boundary value problems