arrayofvh.edp

FreeFem++可以生成高质量的有限元网格。可以用于流体力学

verbosity=1;
mesh Th=square(5,5);
fespace Vh(Th,P1);
Vh u,v;
real[int] X(9);  // array of 9 real
X=5; // fill X with 1
cout << "  norme^2 of X  " <<  sqrt(X' * X) <<  " == 15 \n";
Vh[int] uu(10);  // array of 10 solution 
/*  to do 
mesh[int] aTh(10); // array of 10 meshes 
aTh[1]= square(2,2);
*/ 
int i;
for ( i=0;i<10;i++)
 uu[i]=x+i*y; 

func f= 0;
func g= x*x+y*y*2;
u=0; 
// dcl the problem and solve
solve a(u,v,solver=CG) =
    int2d(Th)(  dx(u)*dx(v) + dy(u)*dy(v)) 
  + int2d(Th) ( v*f ) 
  + on(1,2,3,4,u=g+i); 

cout << "-------------------" << endl;  
plot(u);

// exemple de calcul de semi norme H_1
varf  lap(u,v)  = int2d(Th)(  dx(u)*dx(v) + dy(u)*dy(v) ); 
matrix A= lap(Vh,Vh);
cout <<  " (semi norme H^1)^2 of u =" << (v[]=A*u[])' * u[] << endl; 
cout <<  " (semi norme H^1)^2 of u =" << int2d(Th)(  dx(u)*dx(u) + dy(u)*dy(u) ) << endl; 

for ( i=0;i<10;i++)
 cout << "|x +"<< i <<"y|_H_1 = " << sqrt((v[]=A*uu[i][])' * uu[i][])  << endl;