a_tutorial.edp

FreeFem++可以生成高质量的有限元网格。可以用于流体力学

// This test shows some powerful features of freefem++ on a
// simple example: $-\Delta(u)=1$ in the unit cercle with $u=0$ on the
// border of the unit cercle. this problem has an analytical solution
// u = (1-x^2-y^2)/4
real pi=4*atan(1);
border a(t=0,2*pi){ x = cos(t); y = sin(t);label=1;};

mesh disk = buildmesh(a(50));
plot(disk);
fespace femp1(disk,P1);  
femp1 u,v; 

problem laplace(u,v) = 
    int2d(disk)( dx(u)*dx(v) + dy(u)*dy(v) )     //  bilinear form
  + int2d(disk)( -1*v )                          //  linear form
  + on(1,u=0) ;                                // boundary condition 

laplace; 
femp1 err=u-(1-x^2-y^2)/4;

plot (u,value=true,wait=true);
plot(err,value=true,wait=true);

cout << "error L2=" << sqrt(int2d(disk)( (u-(1-x^2-y^2)/4) ^2) )<< endl;
cout << "error H10=" << sqrt(   int2d(disk)((dx(u)+x/2)^2) 
                              + int2d(disk)((dy(u)+y/2)^2))<< endl;

 disk = adaptmesh(disk,u,err=0.01);
plot(disk,wait=1);

laplace; 

plot (u,value=true,wait=true);
err =u-(1-x^2-y^2)/4;
plot(err,value=true,wait=true);
cout << "error L2=" << sqrt(int2d(disk)( (u-(1-x^2-y^2)/4) ^2) )<< endl;
cout << "error H10=" << sqrt(  int2d(disk)((dx(u)+x/2)^2) 
                             + int2d(disk)((dy(u)+y/2)^2))<< endl;