testfe.edp

FreeFem++可以生成高质量的有限元网格。可以用于流体力学

// exact solution is [x*x,y]  -Delta [x*x,y] = [-2,0]
// This exemple is buggus before version 1.26
{ 
// test of product of same FE
  verbosity = 2;
 mesh Th=square(2,2);
 fespace Vh(Th,P2);
 
 Vh uHx=0;
 Vh uHy=0;
 Vh vHx;
 Vh vHy;
 
 solve  deuxlap([uHx,uHy],[vHx,vHy],solver=CG) =
    int2d(Th)(    dx(uHx)*dx(vHx) + dy(uHx)*dy(vHx)
               +  dx(uHy)*dx(vHy) + dy(uHy)*dy(vHy)  )
    - int2d(Th)( -2* vHx )        
    +  on(1,2,3,4,uHx=x*x,uHy=y);
   // plot(uHx, uHy,wait=1);
    real err2= sqrt( int2d(Th)(square(uHx-x*x)+square(uHy-y)));
    cout << " Error in L2 norme " << err2 << endl ;
    assert(err2 < 1e-10);
}

{ 
// test of product of different  FE
verbosity = 2;
 mesh Th=square(2,2);
 fespace Vh(Th,P2);
 fespace Vh1(Th,P1);
 
 Vh uHx=0;
 Vh1 uHy=0;
 Vh vHx;
 Vh1 vHy;
 
 solve  deuxlap([uHx,uHy],[vHx,vHy],solver=CG) =
    int2d(Th)(    dx(uHx)*dx(vHx) + dy(uHx)*dy(vHx)
               +  dx(uHy)*dx(vHy) + dy(uHy)*dy(vHy)  )
    - int2d(Th)( -2* vHx )        
    +  on(1,2,3,4,uHx=x*x,uHy=y);
   // plot(uHx, uHy,wait=1);
    real err2= sqrt( int2d(Th)(square(uHx-x*x)+square(uHy-y)));
    cout << " Error in L2 norme " << err2 << endl ;
    assert(err2 < 1e-10);
}