High-Accuracy Approximation of High-Rank Derivatives: Isotropic Finite Differences Based on Lattice-Boltzmann Stencils

Figure 3

Isocontours of the local relative errors when numerical solutions of the diffusion equation are computed using second-order accurate finite-difference approximations for the Laplacian. The errors are anisotropic for two of the approximations, (a) the standard five-point stencil and (b) (41) with D2Q9, while for the remaining two, (c) the Mehrstellen approximation and (d) (41) with D2V17, the errors are isotropic. The numerical results conform with the theoretical predictions. The colors are not scaled between the approximations.