# Calculation of discrete weak gradient

**URL:** <https://community.freefem.org/t/calculation-of-discrete-weak-gradient/2468>\
**Category:** General Discussion\
**Created:** [May 17, 2023, 11:37am UTC](https://community.freefem.org/t/calculation-of-discrete-weak-gradient/2468 "2023-05-17T11:37:35Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![freefemuser](https://avatars.discourse-cdn.com/v4/letter/f/e47774/32.png) [@freefemuser](https://community.freefem.org/u/freefemuser)\
**Post date:** [May 17, 2023, 11:37am UTC](https://community.freefem.org/t/calculation-of-discrete-weak-gradient/2468/1 "2023-05-17T11:37:35Z")

</div>

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:  
 ![Screenshot 2023-05-17 163156](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/7/788c9030fb509860080251b67c446a55e5a5fbbc.png)

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.

```auto
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.

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<div class="post-metadata">

**Author:** ![marchywka](https://avatars.discourse-cdn.com/v4/letter/m/ee59a6/32.png) [@marchywka](https://community.freefem.org/u/marchywka)\
**Post date:** [May 17, 2023, 11:54am UTC](https://community.freefem.org/t/calculation-of-discrete-weak-gradient/2468/2 "2023-05-17T11:54:08Z")

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I’m not sure if you can mix and match vector fespaces like that.  
Personally I would start with all scalar fespaces and see  
if that works although there may be better ways to user the vector  
fespaces.  
my FF is down right now with fortran issues or I would run ia  
modified version…

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<div class="post-metadata">

**Author:** ![marchywka](https://avatars.discourse-cdn.com/v4/letter/m/ee59a6/32.png) [@marchywka](https://community.freefem.org/u/marchywka)\
**Post date:** [May 17, 2023, 3:23pm UTC](https://community.freefem.org/t/calculation-of-discrete-weak-gradient/2468/3 "2023-05-17T15:23:06Z")

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I’m new to FF and don’t have a lot of experience with FEM but there are a number  
of things here that are not real common.  
I guess in terms of the FF code, generally you pass 2n parameters to problem solve  
or varf where the first n are the unknowns and the latter are the placeholders for the  
test functions determined by the fespace elements. In any case, div and vn are AFAICT  
identically zero. But do you have more context around (1) and how it  
realtes to the FF code? This appears to have a vector test function with a scalar  
unknown The first two volume integrals can be related by integration by parts.