# Convect function failing

**URL:** <https://community.freefem.org/t/convect-function-failing/1726>\
**Category:** General Discussion\
**Created:** [May 8, 2022, 3:35pm UTC](https://community.freefem.org/t/convect-function-failing/1726 "2022-05-08T15:35:24Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![simbar](https://avatars.discourse-cdn.com/v4/letter/s/dec6dc/32.png) [@simbar](https://community.freefem.org/u/simbar)\
**Post date:** [May 8, 2022, 3:35pm UTC](https://community.freefem.org/t/convect-function-failing/1726/1 "2022-05-08T15:35:24Z")

</div>

Hi everyone, I am currently using FreeFEM to model the kuramoto sivashinsky equation  
 u\_{t}+\nu u\_{xxxx}+u\_{xx}+uu\_{x}=0   
with periuodic spatial and temporal boundary conditions. I am modeling this equation by differentiating u once and then modeling both the ux and uy derivatives. I am trying to use the convect function to handle the u\_{t} and uu\_{x} terms however I always arrive at the error message:

error operator ( \<7E\_Array\>, , \<10LinearCombI7MGauche4C\_F0E\>…

I am not sure what I’m doing wrong here and would appreciate any advice that could be given. The code I am working on is listed below. Thanks in advance!

\begin{verbatim}  
real nu = 1;  
real lambda = 25;  
real dt = 0.05;  
real epsu = 1e-6;  
//mesh  
mesh Th = square(50,50);

//fespace

fespace Vh(Th, P2b,  
periodic = [[0,lambda],[0,lambda]]);  
Vh u=sin(lambda_pi_x)+sin(lambda_pi_y);  
Vh ux = dx(u);  
Vh uy = dy(u);  
Vh v;

for(int n = 0; n\<100; n++){  
Vh uxold = ux;  
Vh uyold = uy;

//problem  
solve ksx(ux, v, init = n, solver = CG, eps = epsu)  
= int2d(Th) (ux_v)  
//+ int2d(Th) (  
//convect([dx(ux), dy(ux)], -dt, ux)v) //convect term causes crash  
+ int2d(Th)(  
dtnu/2_(dxx(ux)\*dxx(v)+dyy(ux)_dyy(v)))  
- int2d(Th)(  
dt/2_(dx(uxold)\*dx(v)+dy(uxold)_dy(v)))  
- int2d(Th)(  
dt/2_(dx(ux)_dx(v)+dy(ux)dy(v)))  
+ int2d(Th)(  
dtnu/2_(dxx(uxold)\*dxx(v)+dyy(uxold)\*dyy(v)))

```
		;
solve ksy(uy, v, init = n, solver = CG, eps = epsu)
  		= int2d(Th) (uy*v)
  		//+ int2d(Th) (
          		// convect([dx(uy), dy(uy)], -dt, uy)*v) //convect term causes crash
  		+ int2d(Th)(
         		 dt*nu/2*(dxx(uy)*dxx(v)+dyy(uy)*dyy(v)))
  		- int2d(Th)(
          		dt/2*(dx(uyold)*dx(v)+dy(uyold)*dy(v)))
 		- int2d(Th)(
          		dt/2*(dx(uy)*dx(v)+dy(uy)*dy(v)))
  		+ int2d(Th)(
        		 dt*nu/2*(dxx(uyold)*dxx(v)+dyy(uyold)*dyy(v)))

                   ;

        //solver here should be laplace u = gradient f where f is (ux,uy), after this I can plot u
        solve ksu(u,v, init = n, solver = CG, eps = epsu)
            = int2d(Th)(dx(u)*dx(v)+dy(u)*dy(v))
	+int2d(Th)((dx(ux)+dy(uy))*v)
	+on(1, u=sin(pi*lambda*x))
	+on(2, u=sin(pi*lambda*y))
	+on(3, u=sin(pi*lambda*x))
	+on(4, u=sin(pi*lambda*y))
	;

plot(u);

```

}  
\end{verbatim}

---

<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 11, 2022, 8:17am UTC](https://community.freefem.org/t/convect-function-failing/1726/2 "2022-05-11T08:17:29Z")

</div>

I all a a C1 finite element in 1d (P3 hermite) it is trivial and after all is trivial.

---

<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 12, 2022, 10:14am UTC](https://community.freefem.org/t/convect-function-failing/1726/3 "2022-05-12T10:14:48Z")

</div>

a first test with the new P3 hermite finite element :

```auto
load "msh3"
load "Element_P3" // for P3
load "Element_P4" // for P3
// u_t + nu u_xxxx + u_xx + u*u_x =0; 
real L= 2*pi;
meshL Th=segment(100,[x*L]);
fespace Vh(Th,P3HL,periodic=[[1],[2]]);
fespace Ph(Th,P3);
Vh [u,ux],[v,vx],[up,upx];// function and derivative
Ph X=x; // for 1d graphic
real nu=1; 
real dt = 0.1; 
[u,ux] = [2+sin(x),cos(x)];// initial guess : function and derivative (need for P3 Hermite interpolation)
for (int i=0; i<100; ++i)
{
	up[]=u[]; 
     solve bilap([u,ux],[v,vx]) =
       int1d(Th)(u*v/dt + nu*dxx(u)*dxx(v) - dx(u)*dx(v) + up*dx(u)*v) 
   - int1d(Th)(up*v/dt);
;
Ph U=u; // to plot the solution 
plot([X[],U[]], cmm=i);
}

```

To use this script you need to install [add new P3 hermite FE in 1d,and P4 Lagrange FE in 1d .. · FreeFem/FreeFem-sources@a811767 · GitHub](https://github.com/FreeFem/FreeFem-sources/commit/a8117678d0e007d921015558c56507d7561afe8d)