Dear experts,
Can you guide me how to implement this in FreeFem++ ?
Many many thanks in advance.
The compatibility condition is
\int_\Omega e^{x+y} + \int_{\partial \Omega} 1/2 e^{x+y} = 0
first find \Omega
after the it is trivial to solve problem with FreeFM.
No the formulation is :
macro grad(u) [dx(u),dy(u)]//
real cc = 0.1,err,eps = 1e-6 ;
err = int2d(Th)(f) + int1d(Th)(g) ;
cout << " err = " << err << endl;
asser(err < 1e-8) ; // compatiblity condition
solve hw2(u,v) = int2d(Th) (grad(u)'*grad(v)+ eps*u*v)
- int1d(Th)(g*v) - int2d(Th)(v*f);
and here the err = 9.34155 => no solution
Thank you so much. It totally makes sense now as the compatibility is not holding true. But is there anyway to adjust the boundary conditions so that it will hold true?
They are 2 ways to solve this compatibility problem multi g buy a other constant cc
real cc = 1;
func f = exp(x+y);
func g = cc*exp(x+y);
cc = int2d(Th)(f)/ int1d(Th)(g);
Other way is find a domain \Omega such \int_\Omega (f)/ \int_{\partial Th}(g)=1
1 Like