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

Figure 5

See the caption of Figure 3. The error for the sixth-order approximation for (a) Section 5 with D2V81 is slightly anisotropic while for (b) Section 5 with D2V141 the error is isotropic. The error for the eighth-order approximation for (c) Section 5 with D2V141 also exhibits small anisotropic patterns. The theoretically predicted isotropy properties are hence numerically confirmed. The colors are not scaled between the approximations.