$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Computing the norm of the error
- \( e^n \) is a mesh function
- Usually we want one number for the error
- Use a norm of \( e^n \)
Norms of a function \( f(t) \):
$$
\begin{align}
||f||_{L^2} &= \left( \int_0^T f(t)^2 dt\right)^{1/2}
\tag{25}\\
||f||_{L^1} &= \int_0^T |f(t)| dt
\tag{26}\\
||f||_{L^\infty} &= \max_{t\in [0,T]}|f(t)|
\tag{27}
\end{align}
$$
