Can you please tell me what is the code of (del^u)/(del n^2), where n is the outward normal.

That is i want to know freefem++ code of second order normal that is u_nn .

Remark, generally we do not use second order derivatives in formulation, we use intergration by part

to get just first order derivatives.

But they is not problem to compute

```
macro D2(u) [[dxx(u),dxy(u)],[dxy(u),dyy(u)]] //
macro dnn(u) ( [N.x,N.y]'* (D2(u) * [N.x,N.y] ))//
```

Thank you sir. I also made a code.

Sir, can you tell me in similar mannar how i write the code for 4th order normal. I have tried but in this case we have to write

(dxxxx(u) *(N.x) ^4+ 14*dxyxy(u) *(N.x) ^2*(N.y) ^2

+dyyyy(u) *(N.y) ^4)

But problem is that dxxxx(u), dyyyy(u) and dxyxy(u)

is not taking by FreeFem++.

We have tried to write it like dxxxx(u) =dxx(dxx(u))

In this fasion. But all are showing error in giving ") ".

Please help sir. It is urgent.

I have tried the following code also.

macro D4(u) [[dxxxx(u), dxyxy(u) ],[ dxyxy(u), dyyyy(u) ]]//

macro dnnnn(u) ([(N.x) ^2, (N.y) ^2]'*D4(u) *[(N.x) ^2, (N.y) ^2]) //

Still it is showing error to write dxxxx(u).

What to do sir???.

I sorry generally the derivative of order 4 is zero for lot of finite element, you have to think about your numerical scheme.