$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\vex}{{v_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
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
