# Execution macro error \* \<10LinearCombI7MGauche4C\_F0E\>

**URL:** https://community.freefem.org/t/execution-macro-error-10linearcombi7mgauche4c-f0e/1744
**Category:** General Discussion
**Created:** [May 14, 2022, 12:39pm UTC](https://community.freefem.org/t/execution-macro-error-10linearcombi7mgauche4c-f0e/1744 "2022-05-14T12:39:20Z")
**Posts on this page:** 3
**Page:** 1

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### Author: ![bomber](https://avatars.discourse-cdn.com/v4/letter/b/5fc32e/32.png) [@bomber](https://community.freefem.org/u/bomber)
#### Post date: [May 14, 2022, 12:39pm UTC](https://community.freefem.org/t/execution-macro-error-10linearcombi7mgauche4c-f0e/1744/1 "2022-05-14T12:39:20Z")

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Hello,  
I’m a new Freefem user;  
I’d like to solve the following equation

∂∆φ/∂t+∂φ/∂x ∂∆φ/∂y-∂φ/∂y ∂∆φ/∂x=0

begin φ a scalar potential;

I implemented the weak formulation of the problem using the freeFEM syntax, unfortunately during the execution the following error appears

> problem turbu(Phi,u,Psi,uu)=int2d(Th)(u_Psi/dt+gradPzgradu(Phi,u) ([dx(Phi), -dy(Phi)]_[dy(u), dx(u)]) erro0ýlr operator \* \<10LinearCombI7MGauche4C\_F0E\>, \<10LinearCombI7MGauche4C\_F0E\>  
> List of choices…

I tried different ways without to reach a right solution but It seems that the problem comes from the macro definition;

please, could anybody give me some help?

Thanks a lot for the time

Best Regards  
Giulio

Ps\> I’m including below the implemented FreeFEM code

int bottom=1;  
int right=2;  
int top=3;  
int left=4;  
int L=2.\*pi;  
int n=60;  
real dt=0.1;  
real T=1.;

//Domain calculation  
border b1(t=0,L){x=t; y=0; label=bottom;};  
border b2(t=0,L){x=L; y=t; label=right;};  
border b3(t=L,0){x=t; y=L; label=top;};  
border b4(t=L,0){x=0; y=t; label=left;};  
// Mesh definition.  
mesh Th = buildmesh(b1(n)+b2(n)+b3(n)+b4(n));  
plot(Th);  
//Space definiton.  
fespace Vh(Th,P1b);  
Vh Phi, Psi;  
fespace Uh(Th,P1);  
Uh u, uu, uold=0;  
//Macro Definition  
macro gradPzgradu(Phi,u) ([dx(Phi), -dy(Phi)]\*[dy(u), dx(u)]) //

//Weak Formulation  
problem turbu(Phi,u,Psi,uu)=int2d(Th)(u_Psi/dt+gradPzgradu(Phi,u)Psi)-int2d(Th)(uoldPsi/dt)+int2d(Th)(u_uu-dx(Phi)\*dx(uu)+dy(Phi)\*dy(uu));//+on(1,2,4, Phi=0.01,u=0)+on(3, Phi=0.02,u=0);  
//plot(u,value=1);

for(real t = 0; t \< 0.02; t += dt){  
uold = u; //equivalent to u^{n-1} = u^n  
turbu; //here the thermic problem is solved;  
plot(Phi);  
}

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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: [May 16, 2022, 11:13am UTC](https://community.freefem.org/t/execution-macro-error-10linearcombi7mgauche4c-f0e/1744/2 "2022-05-16T11:13:47Z")

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> [@bomber](#):
>
> macro gradPzgradu(Phi,u) ([dx(Phi), -dy(Phi)]\*[dy(u), dx(u)]) //

This is non linear imply the error product of unknown term (Gauche term in french).

```auto
erro0ýlr operator * <10LinearCombI7MGauche4C_F0E>, <10LinearCombI7MGauche4C_F0E>

```

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<div class="post-metadata">

### Author: ![bomber](https://avatars.discourse-cdn.com/v4/letter/b/5fc32e/32.png) [@bomber](https://community.freefem.org/u/bomber)
#### Post date: [May 22, 2022, 1:53pm UTC](https://community.freefem.org/t/execution-macro-error-10linearcombi7mgauche4c-f0e/1744/3 "2022-05-22T13:53:18Z")

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Thank you for your answer and for identifying the problem. Do you think that the Fixe-Point and Newton iteration method is adequate to implement the nonlinear part?