# Strong formulation

**URL:** <https://community.freefem.org/t/strong-formulation/1042>\
**Category:** General Discussion\
**Created:** [June 16, 2021, 3:40pm UTC](https://community.freefem.org/t/strong-formulation/1042 "2021-06-16T15:40:03Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![paabl0\_9](https://avatars.discourse-cdn.com/v4/letter/p/c5a1d2/32.png) [@paabl0\_9](https://community.freefem.org/u/paabl0_9)\
**Post date:** [June 16, 2021, 3:40pm UTC](https://community.freefem.org/t/strong-formulation/1042/1 "2021-06-16T15:40:03Z")

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Hi, i need to write this variational problem on its strong formulation.

mesh Th=square(10,10);  
fespace Vh(Th,P1);  
Vh uh,vh; //  
func f=1; //  
func g=0; //  
problem laplace(uh,vh,solver=GMRES,tgv=1e5) = //  
int2d(Th)( dx(uh)_dx(vh) + dy(uh)dy(vh) ) //  
int1d(Th,1)( uhvh) //  
int1d(Th,1)( vh) //  
int2d(Th)( f_vh ) //  
on(2,3,4,uh=g) ; //  
laplace; //  
plot(uh,ps=“LaplaceP1.eps”,value=true); //

Thanks for help.

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<div class="post-metadata">

**Author:** ![frederichecht](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/frederichecht/32/15_2.png) [@frederichecht](https://community.freefem.org/u/frederichecht)\
**Post date:** [June 23, 2021, 12:09pm UTC](https://community.freefem.org/t/strong-formulation/1042/2 "2021-06-23T12:09:55Z")

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$$- \Delta u = f = 1 \mbox{ in } \Omega = ]0,1[^2$$  
remember the border $\Gamma\_i$ is  
i: 1: bottom , 2 right, 3 top , 4 left  
border of the square

on $\Gamma\_1$ we have fourier / robin condtion:  
${\partial(u)\over \partial n} = 1 - u $

On 3 other boundary $\Gamma\_2$ ,$\Gamma\_2$ ,$\Gamma\_4$ the Boundary condition is

u = g = 0

the image of latex :

 ![image](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/1X/94f0c9f0520f03d8fb8947b6ff68426a45abc6f5.png)