Hey y’all!

As prep for my master’s thesis, I’m trying to implement a numerical method for the heat equation using Raviart-Thomas finite elements. While the documentation has a nice example on how to use RT0 finite elements in 2D, I’m having a lot of trouble trying to get them to work in 3D. I naïvely tried to adapt the code in the `LaplaceRT.edp`

example file as such:

## Code

```
load "msh3"
// Parameters
func gd = 1.;
func g1n = 1.;
func g2n = 1.;
func g3n = 1.;
// Mesh
mesh3 Th = cube(10, 10, 10);
// Fespace
fespace Vh(Th, RT03d);
Vh [u1, u2, u3];
Vh [v1, v2, v3];
fespace Ph(Th, P0);
Ph p, q;
// Problem
problem laplaceMixte ([u1, u2, u3, p], [v1, v2, v3, q], solver=GMRES, eps=1.0e-10, tgv=1e30, dimKrylov=150)
= int3d(Th)(
p*q*1e-15 //this term is here to be sure
// that all sub matrix are inversible (LU requirement)
+ u1*v1
+ u2*v2
+ u3*v3
+ p*(dx(v1)+dy(v2)+dz(v3))
+ (dx(u1)+dy(u2)+dz(u3))*q
)
+ int3d(Th) (
q
)
- int2d(Th, 1, 2, 3, 4, 5)(
gd*(v1*N.x + v2*N.y + v3*N.z)
)
+ on(6, u1=g1n, u2=g2n, u3=g3n)
;
// Solve
laplaceMixte;
// Plot
plot([u1, u2, u3], coef=0.1, wait=true, value=true);
plot(p, fill=1, wait=true, value=true);
```

The GMRES solver is not converging, and even if I cut it off prematurely, the plots are empty. What’s going wrong here? And advice would be greatly appreciated. I’m using FreeFEM++ version 4.14.