Discrete L2 norm
= Discrete L2 norm
{title2=$\|U\|_h^2=h^d\sum_j|U_j|^2$}
On a uniform $d$-dimensional spatial grid, the discrete L2 norm weights the squared <Euclidean norm> by the cell volume. It approximates the continuous <L2 norm> and is induced by the <discrete L2 inner product>. A contraction bound in this norm with a mesh-independent constant proves <stability of a numerical method> for the spatially discretized evolution.