Various error measures

• Dream: the true error $e = \uex-u$, but usually impossible
• Must find other error measures that are easier to calculate

• Derive formulas for $u$ in (very) special, simplified cases
• Compute empirical convergence rates for special choices of $\uex$ (usually non-physical $\uex$)
• To what extent does $\uex$ fulfill $\mathcal{L}_\Delta(\uex)=0$?
• It does not fit, but we can measure the error $\mathcal{L}_\Delta(\uex)=R$
• $R$ is the truncation error and it is easy to compute in general, without considering special cases