fem_check13_la.c running 
Given x^2 u''(x) + 2x u'(x) + 3u(x) = 
  3 -(100/3)*x +108*x^2 -80*x^3 
  0<x<1  Boundary u(0) = 1, u(1) = 1 
Analytic solution u(x) = 1 -(20/3)*x +12*x^2 -(16/3)*x^3 
Try 10 points 
F forcing function and exact solution 
i=0, F(  0.000)=  3.000, exact=  1.000 
i=1, F(  0.111)=  0.520, exact=  0.400 
i=2, F(  0.222)=  0.048, exact=  0.053 
i=3, F(  0.333)=  0.926, exact= -0.086 
i=4, F(  0.444)=  2.495, exact= -0.061 
i=5, F(  0.556)=  4.097, exact=  0.086 
i=6, F(  0.667)=  5.074, exact=  0.309 
i=7, F(  0.778)=  4.767, exact=  0.565 
i=8, F(  0.889)=  2.517, exact=  0.810 
i=9, F(  1.000)= -2.333, exact=  1.000 

compute stiffness matrix 
val=-2.55519, for k at i=1, j=0 
val=27.0972, for k at i=1, j=1 
val=-120.609, for k at i=1, j=2 
val=322.605, for k at i=1, j=3 
val=-566.018, for k at i=1, j=4 
val=681.574, for k at i=1, j=5 
val=-570.03, for k at i=1, j=6 
val=325.582, for k at i=1, j=7 
val=-118.212, for k at i=1, j=8 
val=21.1919, for k at i=1, j=9 
val=0.151995, for f at i=1 
val=11.9804, for k at i=2, j=0 
val=-121.669, for k at i=2, j=1 
val=547.252, for k at i=2, j=2 
val=-1463.93, for k at i=2, j=3 
val=2571.87, for k at i=2, j=4 
val=-3098.51, for k at i=2, j=5 
val=2592.13, for k at i=2, j=6 
val=-1480.72, for k at i=2, j=7 
val=537.589, for k at i=2, j=8 
val=-96.3515, for k at i=2, j=9 
val=0.104558, for f at i=2 
val=-32.591, for k at i=3, j=0 
val=329.272, for k at i=3, j=1 
val=-1481.19, for k at i=3, j=2 
val=3960.13, for k at i=3, j=3 
val=-6955.63, for k at i=3, j=4 
val=8381.85, for k at i=3, j=5 
val=-7012.02, for k at i=3, j=6 
val=4005.1, for k at i=3, j=7 
val=-1453.72, for k at i=3, j=8 
val=260.434, for k at i=3, j=9 
val=-0.56941, for f at i=3 
val=58.3042, for k at i=4, j=0 
val=-587.212, for k at i=4, j=1 
val=2644.93, for k at i=4, j=2 
val=-7069.97, for k at i=4, j=3 
val=12412.6, for k at i=4, j=4 
val=-14955.2, for k at i=4, j=5 
val=12512, for k at i=4, j=6 
val=-7145.31, for k at i=4, j=7 
val=2592.52, for k at i=4, j=8 
val=-464.154, for k at i=4, j=9 
val=1.80898, for f at i=4 
val=-72.0647, for k at i=5, j=0 
val=724.441, for k at i=5, j=1 
val=-3264.68, for k at i=5, j=2 
val=8728.59, for k at i=5, j=3 
val=-15322.2, for k at i=5, j=4 
val=18453.2, for k at i=5, j=5 
val=-15434, for k at i=5, j=6 
val=8813.21, for k at i=5, j=7 
val=-3195.87, for k at i=5, j=8 
val=571.617, for k at i=5, j=9 
val=-1.66748, for f at i=5 
val=62.7982, for k at i=6, j=0 
val=-630.499, for k at i=6, j=1 
val=2842.11, for k at i=6, j=2 
val=-7598.82, for k at i=6, j=3 
val=13339.9, for k at i=6, j=4 
val=-16061.5, for k at i=6, j=5 
val=13422.5, for k at i=6, j=6 
val=-7657.29, for k at i=6, j=7 
val=2775.31, for k at i=6, j=8 
val=-495.611, for k at i=6, j=9 
val=2.53703, for f at i=6 
val=-38.7977, for k at i=7, j=0 
val=389.172, for k at i=7, j=1 
val=-1754.51, for k at i=7, j=2 
val=4690.55, for k at i=7, j=3 
val=-8233.17, for k at i=7, j=4 
val=9912.32, for k at i=7, j=5 
val=-8276.76, for k at i=7, j=6 
val=4706.92, for k at i=7, j=7 
val=-1697.46, for k at i=7, j=8 
val=302.866, for k at i=7, j=9 
val=-0.73237, for f at i=7 
val=17.4536, for k at i=8, j=0 
val=-174.949, for k at i=8, j=1 
val=788.788, for k at i=8, j=2 
val=-2108.56, for k at i=8, j=3 
val=3700.51, for k at i=8, j=4 
val=-4454.27, for k at i=8, j=5 
val=3719.76, for k at i=8, j=6 
val=-2109.41, for k at i=8, j=7 
val=746.679, for k at i=8, j=8 
val=-125.952, for k at i=8, j=9 
val=0.83572, for f at i=8 
k computed stiffness matrix, see above 
f computed forcing function, see above 

u computed Galerkin, Ua analytic, error 
u[0]= 1.0000, Ua= 1.0000, err=1.33227e-15 
u[1]= 0.4001, Ua= 0.4001, err=-4.82392e-13 
u[2]= 0.0526, Ua= 0.0526, err=1.44804e-12 
u[3]=-0.0864, Ua=-0.0864, err=1.16721e-12 
u[4]=-0.0608, Ua=-0.0608, err=7.35086e-13 
u[5]= 0.0855, Ua= 0.0855, err=5.22665e-13 
u[6]= 0.3086, Ua= 0.3086, err=3.14304e-13 
u[7]= 0.5647, Ua= 0.5647, err=1.9329e-13 
u[8]= 0.8098, Ua= 0.8098, err=9.86988e-14 
u[9]= 1.0000, Ua= 1.0000, err=0 
                                        maxerr=1.44804e-12, avgerr=4.96301e-13