Page 385 - Process Modelling and Simulation With Finite Element Methods

312 Process Modelling and Simulation with Finite Element Methods

Figure A7. Arrow plot of curl computed for the example F = ( xz, 3xy, x3 ) .

The Lapluciun Operator
For the scalar field Q,

- a2$ a2+ a2$
--+-+7
ax2 ayz az

By parallel with other nabla operators,
div (grad) = V . V

- a* a2 a2
-a,2+p+g

So for shorthand, the operator div(grad) is called the Laplacian and denoted V2.
Typically, the Laplacian is used in differential equations, rather than computed
directly. For instance, Laplace’s equation