function q = cal_debit_2D(U,COOR, CONNEC, NUMER, ADRESS)
// 
[Nelt, Nno] = size(CONNEC);
Npt = length(COOR);

q = 0.;
for iel = 1:Nelt    

   x  = COOR(CONNEC(iel,:),1); y = COOR(CONNEC(iel,:),2);
   u_el = U(ADRESS(iel,:)) 

   for ig=1:Ng    // double boucle pour l'integration numerique
      xg = XG(ig);
      for jg=1:Ng
         yg = XG(jg);
//
// calcul de la matrice jacobienne
//
          [F,DxiFP,DetaFP] = Q1(xg,yg);
          j11 = x(1:4)'*DxiFP; 
          j12 = x(1:4)'*DetaFP;   
          j21 = y(1:4)'*DxiFP;  
          j22 = y(1:4)'*DetaFP;
//
          DT  = [j11 j12; j21 j22];
          jac = det(DT);
//
          [FP,DxiFP,DetaFP] = Q2(xg,yg);
//
          for i=1:Nno
             q  = q + PG(ig)*PG(jg) * u_el(i)*FP(i) * jac;
          end;
      end;
   end;
end;   // fin boucle sur les elements

endfunction


