/usr/share/doc/freefem++/examples/examples++-tutorial/Periodic.edp is in freefem++-doc 3.19.1-1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | mesh Th=square(10,10,[2*x*pi,2*y*pi]);
fespace Vh(Th,P2,periodic=[[2,y],[4,y],[1,x],[3,x]]); // the label 2 and 4 are periodic
// [a1,b1,b2,f1],[b,fb] the degree of freedom of of the border a1,b1,c1 and b are equivalent
// via fonctions f1 and f2
// here full periodic in x and y direction
Vh uh,vh; // unkown and test function.
func f=sin(x+pi/4.)*cos(y+pi/4.); // right hand side function
func g=0; // boundary condition function
problem laplace(uh,vh) = // definion of the problem
int2d(Th)( dx(uh)*dx(vh) + dy(uh)*dy(vh) ) // bilinear form
+ int2d(Th)( -f*vh ) // linear form
;
laplace; // solve the problem plot(uh); // to see the result
plot(uh,ps="period.eps",value=true);
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