# Conditions at the point

**URL:** https://community.freefem.org/t/conditions-at-the-point/181
**Category:** General Discussion
**Created:** [November 19, 2019, 2:57pm UTC](https://community.freefem.org/t/conditions-at-the-point/181 "2019-11-19T14:57:28Z")
**Posts on this page:** 6
**Page:** 1

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### Author: ![PoTS](https://avatars.discourse-cdn.com/v4/letter/p/c67d28/32.png) [@PoTS](https://community.freefem.org/u/PoTS)
#### Post date: [November 19, 2019, 2:57pm UTC](https://community.freefem.org/t/conditions-at-the-point/181/1 "2019-11-19T14:57:28Z")

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Is it possible to provide additional condition for the solution of 2d problem at one point of the boundary (in FreeFem++)? Solution is a vector and the condition includes equality between one component and derivative of the another.

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### Author: ![cmd](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/cmd/32/67_2.png) [@cmd](https://community.freefem.org/u/cmd)
#### Post date: [November 19, 2019, 3:42pm UTC](https://community.freefem.org/t/conditions-at-the-point/181/2 "2019-11-19T15:42:53Z")

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Have you tried using a penalty method? Try penalizing the condition in the weak form with a huge value like 1e30.

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### Author: ![PoTS](https://avatars.discourse-cdn.com/v4/letter/p/c67d28/32.png) [@PoTS](https://community.freefem.org/u/PoTS)
#### Post date: [November 19, 2019, 3:55pm UTC](https://community.freefem.org/t/conditions-at-the-point/181/3 "2019-11-19T15:55:39Z")

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No, I have not such an idea. Thank you so mauch, I’l try.

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### 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: [November 19, 2019, 3:57pm UTC](https://community.freefem.org/t/conditions-at-the-point/181/4 "2019-11-19T15:57:36Z")

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1. in freeFem for thecnical raison you can not put dirichlet boundary condition on 1 points

2. if I have understanse you want to coupled for example u1 and dx(u2) at one point,  
it is possible with penalization but I have idea if this converge. or not.

Frederic Hecht.

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### Author: ![PoTS](https://avatars.discourse-cdn.com/v4/letter/p/c67d28/32.png) [@PoTS](https://community.freefem.org/u/PoTS)
#### Post date: [November 19, 2019, 4:40pm UTC](https://community.freefem.org/t/conditions-at-the-point/181/5 "2019-11-19T16:40:19Z")

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Thank you so much for the response.

I am very beginner in FreeFem++, I rather specialized in PDE theory.

The problem I consider is a 2d elasticity in a domain with a cut (elastic body with a crack).

The Signorini type conditions are imposed on the crack faces.

It seems that ANSYS and COMSOL does not allow to realise variational inequalities in such a problems.

So I learn the FreeFem++ opportunities.

At the one of faces of the crack I have thin inclusion, It is 1d object.

The inclusion has two parts: one of the parts modeling in the framework of elastic Timoshenko beam,

and the second part has a specific properties. So I have joint point between them.

Due to solve variational inequality I use domain decomposition method and

in case without any conditions at the joint point it works satisfactory.

But If I want to get a smooth junction between 2 parts of inclusion additional condition is nesessary at the point.

This is the fragment of code:

```auto
   solve timoshenkosemirigidlame0([u11, u12, phi], [uu11, uu12, pphi], solver=CG)
= int2d(Th1)(
lambda*div(u11,u12) *div(uu11,uu12)
+ 2.*mu*epsilon(u11,u12)'*epsilon(uu11,uu12))
- int1d(Th1, G11)(fh1*uu12)
+ int1d(Th1, gt)(dx(u11)*dx(uu11))
+ int1d(Th1, gs)(dx(u11)*dx(uu11))
+ int1d(Th1, gt)(dx(phi)*dx(pphi)+phi*dx(uu12)+dx(u12)*pphi+phi*pphi+dx(u12)*dx(uu12))
+int1d(Th1, gt)(l22*uu12)
+int1d(Th1, gs)(l22*uu12)
+int1d(Th1, G131, G132)(l11*uu11+l12*uu12)
+ on(G12, u11=0, u12=0)
+ on(G14, u11=0, u12=0);

```

I want to put equality -dx(u12)(0,0)=phi(0,0) in the problem formulation but don’t know how to realise it.

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### 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: [August 9, 2020, 4:31pm UTC](https://community.freefem.org/t/conditions-at-the-point/181/6 "2020-08-09T16:31:43Z")

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me too,  
this formulation is incorrect at continus level, to day no way,  
change the formulation,
