Figure 11

Heat treatment problem: relative errors ${max}_{\mathit{\mu }\in {\Xi }_{\mathrm{train}}}({\Delta }_{N_{\mathit{pr}}}(\mathit{\mu })/\parallel u_{N_{\mathit{pr}}}^{\mathcal{N}}(\mathit{\mu }){\parallel }_X)$ and ${max}_{\mathit{\mu }\in {\Xi }_{\mathrm{train}}}({\Delta }_{N_{\mathit{du}}}(\mathit{\mu })/\parallel {\psi }_{N_{\mathit{du}}}^{\mathcal{N}}(\mathit{\mu }){\parallel }_X)$ as a function of $N^{\mathit{pr}}$ and $N^{\mathit{du}}$ for the RB approximations computed during the greedy procedure, for the primal (left) and the dual (right) problem, respectively. Here ${\Xi }_{\mathrm{train}}$ is a uniform random sample of size $n_{\mathrm{train}}=1\text{,}000$ and the RB tolerance is ${\epsilon }_{\mathrm{tol}}^{\ast }={10}^{-2}$.