Hi,

I’m trying to solve the taylor vortex problem with periodic boundary in the two-dimensional domain x,yϵ[-1,1].

I use the one order time precision discrete the equation, and Initialize the velocity and pressure with analytic solutions.

The procedure as follows:

mesh Th=square(32,32,[-1+2*x,-1+2*y]);

fespace Vh(Th,P2,periodic=[[2,y],[4,y],[1,x],[3,x]]);

fespace Ph(Th,P1,periodic=[[2,y],[4,y],[1,x],[3,x]]);

Vh ux,uy,uxold,uyold,vx,vy,dux,duy;

Ph p,pold,q,dp;

real err=10,eps=1e-6,dt=0.02,errt;

uxold=-cos(pi*x) sin(piy);
uyold=sin(pi*x)

*cos(pi*y);

pold=-(cos(2

*pi*x)+cos(2

*pi*y))/4;

plot([uxold,uyold],wait=1);

solve taylor([ux,uy,p],[vx,vy,q]) =

int2d(Th)(

(ux*vx+uy*vy)/dt

+(uxold*dx(ux)+uyold*dy(ux))*vx
+(uxold*dx(uy)+uyold

*dy(uy))*

-q(dx(ux)+dy(uy))

*vy*

-p(dx(vx)+dy(vy))-p

-q

)

-int2d(Th)((uxold

*vx+uyold*vy)/dt)

;

When running the case, FreeFem++ show that :

Problem build of FEspace (2d) (may be: due to periodic boundary condition missing) FH

The number of DF must be 9216 and it is 9539

I don’t know why, I hope somebody could have a look and give me some advices