@Kitonum 

Dear all, 

I can not use a numerical solution. I need a general solution to insert in a system of equation.

Can I use somethin different, for example Laplace or fourier expansion?

Thanks a lot

@Carl Love 

Thanks nad thanks a lot,

you are my lifesaver.

If I can, a futher qyestion:

Ke:= Matrix(9,9, (i,j)-> int(int(Grad[i].Grad[j], xi= 0..1), eta= 0..1));

it is perfect.

If I have to integrate Grad[i].Grad[j]  only along xi=0 and eta=0..1

How Could I do?

Thanks again

Dear C.,

thanks a lot. 

Now I have created this:

restart;
assume(xi::real, eta::real):
phi[1]:=(2*xi-1)*(xi-1)*(2*eta-1)*(eta-1);
phi[2]:= -4*xi*(xi-1)*(2*eta-1)*(eta-1);
phi[3]:= xi*(2*xi-1)*(2*eta-1)*(eta-1);
phi[4]:= -(8*xi-4)*(xi-1)*eta*(eta-1);
phi[5]:= 16*xi*(xi-1)*eta*(eta-1);
phi[6]:= -4*xi*(2*xi-1)*eta*(eta-1);
phi[7]:= (2*xi-1)*(xi-1)*eta*(2*eta-1);
phi[8]:= -4*xi*(xi-1)*eta*(2*eta-1);
phi[9]:= xi*(2*xi-1)*eta*(2*eta-1);

then I have this cycle

for i from 1 to 9 do
  Grad[i]:=<diff(phi[i],xi),diff(phi[i],eta)>
od;

and then I integrate:

for i from 1 to 9 do
   for j from 1 to 9 do 
      Ke[i,j]:=integrate(integrate(Grad[i].Grad[j],xi=0..1),eta=0..1);
   od;
od;

if I use print(Ke), I am not able to visualize the results correctly. I would like to visualize the matrix to export it.

Do you have some suggestions?

Thanks a lot