We are trying to use freefem++ to address computational aspects of weak Galerkin finite element method.

To do so, in the first step, we need to solve the following problem in the finite dimensional settings which reads as:

We have used the following finite element spaces: For *u0* we are using *P0* elements, *ub* , we are using *P1* elements and for H(Div ,Ω), we are using [P1]^2 elements.

In order to compute the discrete weak gradient we are proceeding as follows:

Note that to calculate the discrete weak Gradient, we need to solve the system (1) in finite dimensional settings.

We are solving the problem in the unit square.

```
int P=10;
mesh Th=square(P,P);
fespace Vh(Th, [P1,P1]);
fespace Wh1(Th, P1);
fespace Wh2(Th, P0);
Wh1 ub,vb; Wh2 u0,v0;
Vh [v1,v2],[w1,w2];
Wh2 div;
Wh1 vn;
div=dx(v1)+dy(v2);
vn = v1*N.x+v2*N.y;
solve dgrad(w1,w2,u0,ub,v1,v2,div,vn)= int2d(Th)(w1*v1+w2*v2) +int2d(Th)(u0*div)- int1d(Th)(ub*vn)+on(1,2,3,4,ub=0) ;
```

But, after compilation, we are observing the following error:

Error umpfack umfpack_di_numeric status 1

Error umfpack_di_solve status 1

– Solve :

min nan max nan

min 0 max 0

min nan max nan

I would be happy if anybody can help me with this.

Thanks in advance.