Hi Kevin,

I think the Jacobian is included in this example (the factor “*x”)

If this can be of any help, below I put another example (for spherical coordinates)

```
/**************************************************/
/* Coordinate dependant differential operators */
/**************************************************/
/* Spherical coordinates in the (r,theta) plane */
/* */
/* r --> x in [0,infty] */
/* theta --> y in [0,pi] */
/* phi --> not */
/* */
/* Jacobian determinant */
/* The det(J) = r^2*sin(theta) --> x^2*sin(y) */
macro Jac()(x^2*sin(y) ) // /* */
/* The gradient operator in spherical coordinates */
/* */
/* d/dr */
/* grad = 1/r*d/dtheta */
/* 1/(r*sin(theta))*d/dphi */
/* */
macro Grad(u) [dx(u),dy(u)/x] // /* */
macro Lap(u,v) (Grad(u)'*Grad(v)) // /* ') */
/**************************************************/
macro Source()(exp(-x^2)*(6-4*x^2) ) //
Vh u,v;
problem Poisson(u,v) = int2d(Th)( Jac*Lap(u,v) )
-int2d(Th)(Jac*Source*v)
+on(3,u=1)
+on(1,u=0) ;
Poisson;
plot(u,fill=1,value=1,wait=1);
```

I’ll put also some brief notes I had some time ago, if this can be of any help.

It is for kind of Laplace-Beltrami operator…Here I use the conventions from

field theory/general relativity (raising indices with the metric)

Let me know if this makes sense to you.

Hope this helps,

Julien