Stokes.edp

// Definition of macros
macro div(u1,u2) (dx(u1)+dy(u2)) //EOM
macro gradugradv(u1,u2,v1,v2) (dx(u1)*dx(v1) + dy(u1)*dy(v1) + dx(u2)*dx(v2) + dy(u2)*dy(v2)) //EOM


// Create mesh
mesh Th = square(50,50);

// Definition of spaces
fespace Vh(Th, [P2, P2, P1]); 

func f=1;

// Variational formulation
varf Stokes([u, uY, uP],[v, vY, vP]) = int2d(Th)(gradugradv(u,uY,v,vY) - uP*div(v,vY) + vP*div(u,uY) + 1e-8*uP*vP)
		//- int1d(Th, 3)(1e30*(u*v + uY*vY)) 
		//- int1d(Th, 3)(1e30*v)
		//- int1d(Th,1,2,4)(1e30*(u*v + uY*vY))
		 + on(3, u=1, uY=0) + on(1, 2, 4, u=0, uY=0)
		 ;

varf Lagrange([u, uY, uP],[v, vY, vP]) = int2d(Th)(vP);

matrix MStokes = Stokes(Vh, Vh, tgv = -1);
real[int] bStokes = Stokes(0, Vh, tgv = -10);


real[int] Lag = Lagrange(0, Vh);

matrix MFinal = [[MStokes, Lag], [Lag', 1]];
set(MFinal, solver=sparsesolver);

real[int] bfinal(Vh.ndof + 1);
bfinal(0:Vh.ndof-1) = bStokes(0:Vh.ndof-1);
bfinal(Vh.ndof) = 0;

Vh [uEF, uEFY, uEFP];

uEF[] = MStokes^-1*bStokes;

plot([uEF, uEFY], cmm = "Velocity", value = 1);
plot([uEFP], cmm = "Pressure", value = 1, fill = 1);

cout<<"Mean pressure: "<<int2d(Th)(uEFP)<<endl;