# What is $D_i^h$?

I'm looking at solution seven in here.

They write $v=-D_i^{-h}D_i^h u$ $0<|h|<<1$

What is $D_i^h$? They use $\nabla$ for the gradient, so I don't think it is the $i^{th}$ component of the gradient. I don't think it is $\partial_i$, as in taking $\frac{\partial}{\partial x_i}$ since then I wouldn't know what taking $\partial_i^h$ would possibly mean, since $0<h<1$.

Any ideas?

• It's a discrete difference approximation to the $i^{\text{th}}$ partial derivative of $u$. Jul 17 '17 at 4:43

It's a discrete difference approximation to the $i^{\text{th}}$ partial derivative of $u$.
See $5.8$ of Evans.