A linear interpolation of the vector field components is not divergence-free. Hence the linear component-wise interpolation is intrinsically wrong for vector fields which are solutions of a divergence-free differential equation (like, e.g. a Laplace equation). On the other hand, the ``real divergence'' may as well be underrepresented by the linear interpolation. The same holds true for the vortex component of the vector field.
However, the error made is smaller for better grid quality and a numerical scheme using the same linear interpolation is inferior with respect to accuracy and computational complexity.
Figure 5.4 shows a generated flowline which starts within a
2-simplex and approaches a vortex located inside the triangle.
This situation can be
handled, e.g., by limiting the number of iterations over 
in
Algorithm 5.1.
