= Discrete Sobolev norm
{title2=$\|W\|_{1,h}^2=h\sum_{i=1}^{N-1}|W_i|^2+h\sum_{i=1}^N|D_h^-W_i|^2$}
A discrete Sobolev norm combines weighted <norms> of nodal values and their <finite differences>. For a real sequence $W_0,\ldots,W_N$ with zero endpoints, the displayed expression is a <norm>: it is the Euclidean <norm> of one vector containing both weighted lists, and zero <norm> forces all nodal values to vanish. It approximates the <Sobolev space> $H^1$ <norm>. Endpoint weights or prescribed zero endpoints must be specified when calling a discrete expression a <norm>.
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