fem_check22_la.f90 running
 solve uxx(x,y) + 2 uxy(x,y) + 3 uyy(x,y) +
       4 ux(x,y)  + 5 uy(x,y)  + 6 u(x,y) = c(x,y)
 boundary conditions computed using u(x)
 analytic solution may be given by u(x) = x^3 + y^3 + xy + 1
 Gauss-Legendre integration used
  
 xmin= 0.000000000000000 , ymin = 0.000000000000000
 xmax= 1.00000000000000 , ymax = 1.00000000000000
 nx= 4 , ny = 4
 x grid and analytic solution, at ymin
 i= 1 , Ua( 0.000000000000000 )= 1.00000000000000
 i= 2 , Ua( 0.333333333333333 )= 1.03703703703704
 i= 3 , Ua( 0.666666666666667 )= 1.29629629629630
 i= 4 , Ua( 1.00000000000000 )= 2.00000000000000
  
 y grid and analytic solution, at xmin
 ii= 1 , Ua( 0.000000000000000 )= 1.00000000000000
 ii= 2 , Ua( 0.333333333333333 )= 1.03703703703704
 ii= 3 , Ua( 0.666666666666667 )= 1.29629629629630
 ii= 4 , Ua( 1.00000000000000 )= 2.00000000000000
  
solution at i=1, x= 0.000, ii=1, y= 0.000 is   1.000
solution at i=1, x= 0.000, ii=2, y= 0.333 is   1.037
solution at i=1, x= 0.000, ii=3, y= 0.667 is   1.296
solution at i=1, x= 0.000, ii=4, y= 1.000 is   2.000
solution at i=2, x= 0.333, ii=1, y= 0.000 is   1.037
solution at i=2, x= 0.333, ii=2, y= 0.333 is   1.185
solution at i=2, x= 0.333, ii=3, y= 0.667 is   1.556
solution at i=2, x= 0.333, ii=4, y= 1.000 is   2.370
solution at i=3, x= 0.667, ii=1, y= 0.000 is   1.296
solution at i=3, x= 0.667, ii=2, y= 0.333 is   1.556
solution at i=3, x= 0.667, ii=3, y= 0.667 is   2.037
solution at i=3, x= 0.667, ii=4, y= 1.000 is   2.963
solution at i=4, x= 1.000, ii=1, y= 0.000 is   2.000
solution at i=4, x= 1.000, ii=2, y= 0.333 is   2.370
solution at i=4, x= 1.000, ii=3, y= 0.667 is   2.963
solution at i=4, x= 1.000, ii=4, y= 1.000 is   4.000
boundary i=1, x= 0.000, ii=1, y= 0.000 is    1.00000
boundary i=1, x= 0.000, ii=4, y= 1.000 is    2.00000
boundary i=2, x= 0.333, ii=1, y= 0.000 is    1.03704
boundary i=2, x= 0.333, ii=4, y= 1.000 is    2.37037
boundary i=3, x= 0.667, ii=1, y= 0.000 is    1.29630
boundary i=3, x= 0.667, ii=4, y= 1.000 is    2.96296
boundary i=4, x= 1.000, ii=1, y= 0.000 is    2.00000
boundary i=4, x= 1.000, ii=4, y= 1.000 is    4.00000
boundary i=1, x= 0.000, ii=1, y= 0.000 is    1.00000
boundary i=4, x= 1.000, ii=1, y= 0.000 is    2.00000
boundary i=1, x= 0.000, ii=2, y= 0.333 is    1.03704
boundary i=4, x= 1.000, ii=2, y= 0.333 is    2.37037
boundary i=1, x= 0.000, ii=3, y= 0.667 is    1.29630
boundary i=4, x= 1.000, ii=3, y= 0.667 is    2.96296
boundary i=1, x= 0.000, ii=4, y= 1.000 is    2.00000
boundary i=4, x= 1.000, ii=4, y= 1.000 is    4.00000
 calling gaulegf npx= 48
 calling gaulegf npy= 48
 xx(1)= 0.000614496373786910 , xx(2)= 0.00323491386682462 , wx(1)= 0.00157667302615285 , wx(2)= 0.00366377695063813
 yy(1)= 0.000614496373786910 , yy(2)= 0.00323491386682462 , wy(1)= 0.00157667302615285 , wy(2)= 0.00366377695063813
 galk(xx(2),yy(2),2,2,2,2)= 0.128400249772051
 galf(xx(2),yy(2),2,2)= 0.00676139860687470
 compute stiffness matrix
Legendre integration=     1.77202 at i=2, j=1, ii=2, jj=1
Legendre integration=    -1.04969 at i=2, j=1, ii=2, jj=2
Legendre integration=     0.06070 at i=2, j=1, ii=2, jj=3
Legendre integration=     0.05269 at i=2, j=1, ii=2, jj=4
Legendre integration=    -0.62552 at i=2, j=1, ii=3, jj=1
Legendre integration=     2.34967 at i=2, j=1, ii=3, jj=2
Legendre integration=    -1.04969 at i=2, j=1, ii=3, jj=3
Legendre integration=     0.16126 at i=2, j=1, ii=3, jj=4
Legendre integration=     3.59334 at i=2, j=2, ii=2, jj=1
Legendre integration=   -15.77020 at i=2, j=2, ii=2, jj=2
Legendre integration=    10.95360 at i=2, j=2, ii=2, jj=3
Legendre integration=    -1.95888 at i=2, j=2, ii=2, jj=4
Legendre integration=    -0.80173 at i=2, j=2, ii=3, jj=1
Legendre integration=     7.04824 at i=2, j=2, ii=3, jj=2
Legendre integration=   -15.77020 at i=2, j=2, ii=3, jj=3
Legendre integration=     6.34156 at i=2, j=2, ii=3, jj=4
Legendre integration=    -1.29533 at i=2, j=3, ii=2, jj=1
Legendre integration=     5.87663 at i=2, j=3, ii=2, jj=2
Legendre integration=     0.19294 at i=2, j=3, ii=2, jj=3
Legendre integration=    -0.57960 at i=2, j=3, ii=2, jj=4
Legendre integration=     0.49075 at i=2, j=3, ii=3, jj=1
Legendre integration=    -3.41951 at i=2, j=3, ii=3, jj=2
Legendre integration=     5.87663 at i=2, j=3, ii=3, jj=3
Legendre integration=     1.24677 at i=2, j=3, ii=3, jj=4
Legendre integration=     0.04224 at i=2, j=4, ii=2, jj=1
Legendre integration=    -0.33888 at i=2, j=4, ii=2, jj=2
Legendre integration=    -1.06416 at i=2, j=4, ii=2, jj=3
Legendre integration=     0.35633 at i=2, j=4, ii=2, jj=4
Legendre integration=    -0.06796 at i=2, j=4, ii=3, jj=1
Legendre integration=     0.36781 at i=2, j=4, ii=3, jj=2
Legendre integration=    -0.33888 at i=2, j=4, ii=3, jj=3
Legendre integration=    -0.96543 at i=2, j=4, ii=3, jj=4
Legendre integration=    -0.67133 at i=3, j=1, ii=2, jj=1
Legendre integration=     0.58684 at i=3, j=1, ii=2, jj=2
Legendre integration=     0.03513 at i=3, j=1, ii=2, jj=3
Legendre integration=    -0.05510 at i=3, j=1, ii=2, jj=4
Legendre integration=     0.24061 at i=3, j=1, ii=3, jj=1
Legendre integration=    -0.96291 at i=3, j=1, ii=3, jj=2
Legendre integration=     0.58684 at i=3, j=1, ii=3, jj=3
Legendre integration=     0.03099 at i=3, j=1, ii=3, jj=4
Legendre integration=     1.11298 at i=3, j=2, ii=2, jj=1
Legendre integration=     2.75235 at i=3, j=2, ii=2, jj=2
Legendre integration=    -3.51715 at i=3, j=2, ii=2, jj=3
Legendre integration=     0.80897 at i=3, j=2, ii=2, jj=4
Legendre integration=    -0.55068 at i=3, j=2, ii=3, jj=1
Legendre integration=     1.07165 at i=3, j=2, ii=3, jj=2
Legendre integration=     2.75235 at i=3, j=2, ii=3, jj=3
Legendre integration=    -2.11618 at i=3, j=2, ii=3, jj=4
Legendre integration=     3.59334 at i=3, j=3, ii=2, jj=1
Legendre integration=   -15.77020 at i=3, j=3, ii=2, jj=2
Legendre integration=    10.95360 at i=3, j=3, ii=2, jj=3
Legendre integration=    -1.95888 at i=3, j=3, ii=2, jj=4
Legendre integration=    -0.80173 at i=3, j=3, ii=3, jj=1
Legendre integration=     7.04824 at i=3, j=3, ii=3, jj=2
Legendre integration=   -15.77020 at i=3, j=3, ii=3, jj=3
Legendre integration=     6.34156 at i=3, j=3, ii=3, jj=4
Legendre integration=     0.07729 at i=3, j=4, ii=2, jj=1
Legendre integration=     1.14888 at i=3, j=4, ii=2, jj=2
Legendre integration=     2.67150 at i=3, j=4, ii=2, jj=3
Legendre integration=    -0.92445 at i=3, j=4, ii=2, jj=4
Legendre integration=     0.10733 at i=3, j=4, ii=3, jj=1
Legendre integration=    -0.81077 at i=3, j=4, ii=3, jj=2
Legendre integration=     1.14888 at i=3, j=4, ii=3, jj=3
Legendre integration=     2.52778 at i=3, j=4, ii=3, jj=4
Legendre integration=     1.99045 at i=2, ii=2
Legendre integration=     5.64750 at i=2, ii=3
Legendre integration=     4.46625 at i=3, ii=2
Legendre integration=     8.42705 at i=3, ii=3
 k computed stiffness matrix, see above
 f computed forcing function, see above
  
 ug computed Galerkin, Ua analytic, error
ug(1,1)= 1.0000, Ua= 1.0000, err=  0.8881784E-15
ug(1,2)= 1.0370, Ua= 1.0370, err=  0.6661338E-15
ug(1,3)= 1.2963, Ua= 1.2963, err=  0.0000000E+00
ug(1,4)= 2.0000, Ua= 2.0000, err=  0.0000000E+00
ug(2,1)= 1.0370, Ua= 1.0370, err=  0.1110223E-14
ug(2,2)= 1.1852, Ua= 1.1852, err= -0.8437695E-14
ug(2,3)= 1.5556, Ua= 1.5556, err= -0.5107026E-14
ug(2,4)= 2.3704, Ua= 2.3704, err=  0.0000000E+00
ug(3,1)= 1.2963, Ua= 1.2963, err= -0.4440892E-15
ug(3,2)= 1.5556, Ua= 1.5556, err= -0.9769963E-14
ug(3,3)= 2.0370, Ua= 2.0370, err= -0.6217249E-14
ug(3,4)= 2.9630, Ua= 2.9630, err=  0.0000000E+00
ug(4,1)= 2.0000, Ua= 2.0000, err=  0.0000000E+00
ug(4,2)= 2.3704, Ua= 2.3704, err=  0.0000000E+00
ug(4,3)= 2.9630, Ua= 2.9630, err=  0.0000000E+00
ug(4,4)= 4.0000, Ua= 4.0000, err=  0.0000000E+00
            maxerr= 9.76996261670138E-15 , avgerr= 2.04003480774873E-15
 end fem_check22_la.f90