example21.edp

// example21.edp
// from membranerror.edp
// modified: plot error as field
//           all Dirichlet b.c.
verbosity=0;

real theta = 4.*pi/3.;
real a=1., b=1.; // ellipse is a circle here
border Gamma1(t=0.0,theta)    { x = a * cos(t); y = b*sin(t); }
border Gamma2(t=theta,2.0*pi) { x = a * cos(t); y = b*sin(t); }


func f = -4.0*( cos(x^2 + y^2 - 1.0) - (x^2 + y^2)*sin(x^2 + y^2 - 1.0));
func phiexact = sin(x^2+y^2-1.0);

load "Element_P3"

// compute error on a sequence of meshes
int meshes=4, mshdensity=1;
real[int] L2error(meshes);
for ( int n=0; n<meshes; n++){
  mesh Th = buildmesh( Gamma1(40*mshdensity) + Gamma2(20*mshdensity) );
  mshdensity *= 2;
  fespace Vh(Th, P3); 
  Vh phi,w;
  
  solve laplace(phi, w, solver=UMFPACK) = 
    int2d(Th)( dx(phi) * dx(w) + dy(phi) * dy(w))
    //- int2d(Th)( f*w ) + on(Gamma2,phi=phiexact)+ on(Gamma1, phi=phiexact);
    - int2d(Th)( f*w ) + on(Gamma2, phi=0)+ on(Gamma1, phi=0);

  phi=(phi-phiexact);

  plot(Th, phi, wait=true, fill=true); //Plot Th and phi
  
  // compute error
  L2error[n]= sqrt( int2d(Th)( (phi)^2 ) );
}

// print errors
for (int n=0; n<meshes; n++){
  cout << " L2error " << n << " = "<<  L2error[n] <<endl;
}

// print convergence rates
for (int n=1; n<meshes; n++){
  cout <<" convergence rate = "<< log( L2error[n-1] / L2error[n] )/log(2.)
       <<endl;
}