10.1.1 Uniform metric aligned with axes

The metric tensor is diagonal and defined on each vertex $P$ in the following way:

$${\cal M}(P) = \left( \begin{array}{ccc} \frac{1}{\alpha^2 h^2... ...\beta^2 h^2}&0\\ 0&0&\frac{1}{\gamma^2 h^2} \end{array}\right)$$

The edges length in the direction $x$ (resp. $y$ et $z$) is $\alpha h$ (resp. $\beta h$ et $\delta h$)

The initial mesh can be one of those represented on the Figure 1. The Figure 2 shows some volumic cuts on adapted meshes for several $\alpha$, $\beta$, $\delta$ values.

Figure 1: Volumic cuts in initial meshes.

Figure 2: Volumic cut in adapted meshes: in the left top $\alpha =2$, $\beta = 1$ et $\gamma = 1$ ; in the right top $\alpha =1$, $\beta = 5$ et $\gamma = 1$ ; on the bottom $\alpha =1$, $\beta = 1$ et $\gamma = 10$ .

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