Fig. 1.

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Results of the SPH evaluation of the test profiles A, B, and C using different VEs. Top row: density profiles of models A (Gaussian), B (Inverted-Gaussian), and C (Wall), of Table 1, calculated with X1 using p = 0.0 (magenta) and p = 0.8 (blue) in Eq. (13). Crosses (×) in black are for X2 (Eq. (15), with p = 1) and points in light blue are the analytic values. Central row: E1 (partition of unity) error for the same three profiles following the same color schemes, with the black lines for X2 with p = 1. Bottom row: same as central row but for error E2 = |⟨Δx⟩|/h.
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