$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\vex}{{v_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Empirical verification of the truncation error (2)
- Assume \( R^n = C\Delta t^r \)
- \( C \) and \( r \) will vary with \( n \) - must estimate
\( r \) for each mesh point
- Use a sequence of meshes with \( N_t = 2^{-k}N_0 \) intervals, \( k=1,2,\ldots \)
- Transform \( R^n \) data to the coarsest mesh and estimate \( r \) for
each coarse mesh point
See the text
for more details and an implementation.
