[petsc-users] FEM on 2D poisson equation

[Jed Brown]

Olivier Bonnefon <olivier.bonnefon at avignon.inra.fr> writes:

> Hello,
>
> You are right. I have to define the Jacobian function of the variational 
> formulation. I'm using snes and the petsFem struc (like in ex12).
>
> I need some information about the petscFem struct. I didn't find any 
> document about that, is there one ?
>
> The field f0Funcs is used for the term \int f_0(u,gradu,x)*v
> The field f1Funcs is used for the term \int f_1(u,gradu,x).grad v
>
> Are f0 and f1 used for the rhs of the linearized problem ?

We think about these problems as being nonlinear whether they are or
not.  For a linear problem, you can apply one iteration of Newton's
method using '-snes_type ksponly'.  The Jacobian consists of the
derivatives of f_0 and f_1 with respect to u.

> But what about g0,g1,g2 and g3 functions? I guess I have to use it to 
> define the Jacobian ?

Those are the derivatives of the f_0 and f_1.

For example, see the notation in Eq. 3 and 5 of this paper:

http://59A2.org/na/Brown-EfficientNonlinearSolversNodalHighOrder3D-2010.pdf
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