// example28.edp, from file chapt3/convects.edp
// With Discontinuous Galerkin
border C(t=0, 2*pi) { x=cos(t);  y=sin(t); };
mesh Th = buildmesh(C(100));
fespace Vh(Th,P1dc);

Vh w, ccold, v1 = y, v2 = -x, cc = exp(-10*( (x-0.3)^2 + (y-0.3)^2) );
real u, alpha=0.5,  dt = 0.05;

macro n()(N.x*v1 + N.y*v2) //

problem  Adual(cc, w) = int2d(Th)( (cc/dt + (v1*dx(cc) + v2*dy(cc)) )*w )
  + intalledges(Th)( (1-nTonEdge)*w*( alpha*abs(n) - n/2 )*jump(cc) )
//  - int1d(Th,C)( (n(u)<0)*abs(n(u) )*cc*w)  // unused: cc=0 on d(Omega)^-
  - int2d(Th)( ccold*w/dt );

real [int] viso=[-0.1, 0, 0.5, 0.1, 0.5, 0.2, 0.25, 0.3, 0.35, 0.4, 
                 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.9, 1];

for (real t=0; t< 2*pi ; t+=dt){
  ccold=cc; 
  Adual;
  plot(cc, fill=true, dim=3, viso=viso, 
   cmm="t="+t + ", min=" + cc[].min + ", max=" +  cc[].max);
};

plot(cc,wait=true,fill=false,value=true,viso=viso,
  cmm="example28, min=" + cc[].min + ", max=" +  cc[].max);