- From $|u_h - u| \leq Ch^p$, write  $u - u_h = Ch^p + \mathcal{O}(h^{p+1})$. Transform it to a log-log plot to have the straight line $\log|u_h - u| = p\log(h) +\log|C| + \mathcal{O}(h)$. 
- The convergence rate $p$ is the slope. If exact solution is known, just like that; otherwise, choose $u_h$ as a reference solution by making $h$ as small as possible so that we have a fine mesh (high refinement level). Then, follow the steps above.
- Log-log plots usually relate _refinement factor_ x _L2-norm error_.

- Consider the rel. error the vector ${\bf e} = \frac{ {\bf u} - {\bf u}_h}{\bf u}$. 
- Assume ${\bf u}$ a vector whose $j$-th component is the L2-norm of the mesh quantity over the $n$-dimensional space, i.e. $u_j = \big(\sum_{i=1}^n u_i^2\big)^{1/2}$. Repeat for ${\bf u}_h$, the approximate solution.
- Then, for each mesh node $j$, the $j$-th component of ${\bf e}$ is $e_j = \frac{u_j - u_{h,j}}{u_j}$, for $i = 1,2,\ldots,N$, where $N$ is the number of mesh nodes.
- Finally, we can compute the L2-norm integral error in terms of nodal values by doing $\big( \int_{\Omega} {\bf e}^2 \, d\Omega \big)^{1/2} \approx \big( \sum_{j=1}^N e_j^2 \big)^{1/2}$.

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