fem_nl12_la.c running 
solve Dc*ux(x) + E(x)*(-ux(x)/u(x)^2 - Fc*uxx(x) = f(x)
      f(x) = -2
      Dc = 1
      Fc = 1
      E(X) = (x^2+1)^2
Analytic solution u(x) = x^2+1 
xmin= 1.00000000000000E+00, xmax= 2.00000000000000E+00
nx= 10 points including boundary
x grid and analytic solution 
i= 1, Ua(  1.00000)=  2.00000
i= 2, Ua(  1.11111)=  2.23457
i= 3, Ua(  1.22222)=  2.49383
i= 4, Ua(  1.33333)=  2.77778
i= 5, Ua(  1.44444)=  3.08642
i= 6, Ua(  1.55556)=  3.41975
i= 7, Ua(  1.66667)=  3.77778
i= 8, Ua(  1.77778)=  4.16049
i= 9, Ua(  1.88889)=  4.56790
i= 10, Ua(  2.00000)=  5.00000

calling gaulegf np:= 24
compute stiffness matrix
Legendre integration=-7.76834147375338E+02, at i= 2, j= 1
Legendre integration= 2.99479195239635E+02, at i= 2, j= 2
Legendre integration=-2.62833555491882E+02, at i= 2, j= 3
Legendre integration= 3.10120107508759E+02, at i= 2, j= 4
Legendre integration=-3.37005805711302E+02, at i= 2, j= 5
Legendre integration= 2.93888982152925E+02, at i= 2, j= 6
Legendre integration=-2.29822022105560E+02, at i= 2, j= 7
Legendre integration= 2.82515002821033E+02, at i= 2, j= 8
Legendre integration=-1.00984939388738E+03, at i= 2, j= 9
Legendre integration= 9.94593456464174E+03, at i= 2, j= 10
Legendre integration=-3.51361607142845E-01, i= 2
Legendre integration=-8.89700460066891E+04, at i= 3, j= 1
Legendre integration= 4.24147642540073E+03, at i= 3, j= 2
Legendre integration= 6.69267117248217E+02, at i= 3, j= 3
Legendre integration=-1.31596353379190E+03, at i= 3, j= 4
Legendre integration= 1.56792969496315E+03, at i= 3, j= 5
Legendre integration=-1.86251355848503E+03, at i= 3, j= 6
Legendre integration= 2.84482204629459E+03, at i= 3, j= 7
Legendre integration=-7.26558108834729E+03, at i= 3, j= 8
Legendre integration= 3.38379797032462E+04, at i= 3, j= 9
Legendre integration=-3.53109234445447E+05, at i= 3, j= 10
Legendre integration=-2.41071428571476E-02, i= 3
Legendre integration= 9.50973662673217E+04, at i= 4, j= 1
Legendre integration=-6.03338594020673E+03, at i= 4, j= 2
Legendre integration=-1.15883671986035E+02, at i= 4, j= 3
Legendre integration= 1.25824614385365E+03, at i= 4, j= 4
Legendre integration=-1.69866349492619E+03, at i= 4, j= 5
Legendre integration= 1.89161031911898E+03, at i= 4, j= 6
Legendre integration=-2.37903449004793E+03, at i= 4, j= 7
Legendre integration= 5.22161107554986E+03, at i= 4, j= 8
Legendre integration=-2.37197979025678E+04, at i= 4, j= 9
Legendre integration= 2.50590118177996E+05, at i= 4, j= 10
Legendre integration=-4.31785714285709E-01, i= 4
Legendre integration= 6.43126997408476E+04, at i= 5, j= 1
Legendre integration=-6.37129119733847E+03, at i= 5, j= 2
Legendre integration= 1.96663015392987E+03, at i= 5, j= 3
Legendre integration=-1.65737222132017E+03, at i= 5, j= 4
Legendre integration= 1.80978454375097E+03, at i= 5, j= 5
Legendre integration=-1.67632041382590E+03, at i= 5, j= 6
Legendre integration= 1.19743706236327E+03, at i= 5, j= 7
Legendre integration=-5.26169560192861E+02, at i= 5, j= 8
Legendre integration=-1.19953262991661E+03, at i= 5, j= 9
Legendre integration= 2.26281439561120E+04, at i= 5, j= 10
Legendre integration=-1.28973214285717E-01, i= 5
Legendre integration=-7.92400633411781E+04, at i= 6, j= 1
Legendre integration= 7.77091957427418E+03, at i= 6, j= 2
Legendre integration=-2.18187135999970E+03, at i= 6, j= 3
Legendre integration= 1.65590662953312E+03, at i= 6, j= 4
Legendre integration=-1.81498580813220E+03, at i= 6, j= 5
Legendre integration= 1.77755420197826E+03, at i= 6, j= 6
Legendre integration=-1.35374271227488E+03, at i= 6, j= 7
Legendre integration= 6.73104353330301E+02, at i= 6, j= 8
Legendre integration= 1.14935209779023E+03, at i= 6, j= 9
Legendre integration=-2.44937260924500E+04, at i= 6, j= 10
Legendre integration=-1.28973214285715E-01, i= 6
Legendre integration=-4.23242635813591E+05, at i= 7, j= 1
Legendre integration= 3.88940764757233E+04, at i= 7, j= 2
Legendre integration=-7.36743113837517E+03, at i= 7, j= 3
Legendre integration= 1.70226965964489E+03, at i= 7, j= 4
Legendre integration= 4.70574415095442E+01, at i= 7, j= 5
Legendre integration=-7.30015333796070E+02, at i= 7, j= 6
Legendre integration= 1.11350160746218E+03, at i= 7, j= 7
Legendre integration=-2.83753768072063E+03, at i= 7, j= 8
Legendre integration= 1.71150448968844E+04, at i= 7, j= 9
Legendre integration=-2.23577390711452E+05, at i= 7, j= 10
Legendre integration=-4.31785714285710E-01, i= 7
Legendre integration= 9.62336735131987E+05, at i= 8, j= 1
Legendre integration=-9.15909639563218E+04, at i= 8, j= 2
Legendre integration= 1.89082016264388E+04, at i= 8, j= 3
Legendre integration=-6.14992942551793E+03, at i= 8, j= 4
Legendre integration= 2.65145727246950E+03, at i= 8, j= 5
Legendre integration=-1.46460988232292E+03, at i= 8, j= 6
Legendre integration= 1.01346173139035E+03, at i= 8, j= 7
Legendre integration= 4.07397498357274E+02, at i= 8, j= 8
Legendre integration=-1.54361078679408E+04, at i= 8, j= 9
Legendre integration= 2.74747655154431E+05, at i= 8, j= 10
Legendre integration=-2.41071428571480E-02, i= 8
Legendre integration=-3.54252325465138E+04, at i= 9, j= 1
Legendre integration= 3.40747724996364E+03, at i= 9, j= 2
Legendre integration=-6.64749859244103E+02, at i= 9, j= 3
Legendre integration= 1.06508160863423E+02, at i= 9, j= 4
Legendre integration= 1.18042006245139E+02, at i= 9, j= 5
Legendre integration=-2.07316923215356E+02, at i= 9, j= 6
Legendre integration= 1.77906430868851E+02, at i= 9, j= 7
Legendre integration=-9.88859505192805E+01, at i= 9, j= 8
Legendre integration= 2.45471724565266E+02, at i= 9, j= 9
Legendre integration=-5.89916159914564E+03, at i= 9, j= 10
Legendre integration=-3.51361607142845E-01, i= 9
k computed stiffness matrix
i= 1, j= 1, k(i,j)= 1.00000000000000E+00
i= 1, j= 2, k(i,j)= 0.00000000000000E+00
i= 1, j= 3, k(i,j)= 0.00000000000000E+00
i= 1, j= 4, k(i,j)= 0.00000000000000E+00
i= 1, j= 5, k(i,j)= 0.00000000000000E+00
i= 1, j= 6, k(i,j)= 0.00000000000000E+00
i= 1, j= 7, k(i,j)= 0.00000000000000E+00
i= 1, j= 8, k(i,j)= 0.00000000000000E+00
i= 1, j= 9, k(i,j)= 0.00000000000000E+00
i= 1, j= 10, k(i,j)= 0.00000000000000E+00
i= 2, j= 1, k(i,j)=-7.76834147375338E+02
i= 2, j= 2, k(i,j)= 2.99479195239635E+02
i= 2, j= 3, k(i,j)=-2.62833555491882E+02
i= 2, j= 4, k(i,j)= 3.10120107508759E+02
i= 2, j= 5, k(i,j)=-3.37005805711302E+02
i= 2, j= 6, k(i,j)= 2.93888982152925E+02
i= 2, j= 7, k(i,j)=-2.29822022105560E+02
i= 2, j= 8, k(i,j)= 2.82515002821033E+02
i= 2, j= 9, k(i,j)=-1.00984939388738E+03
i= 2, j= 10, k(i,j)= 9.94593456464174E+03
i= 3, j= 1, k(i,j)=-8.89700460066891E+04
i= 3, j= 2, k(i,j)= 4.24147642540073E+03
i= 3, j= 3, k(i,j)= 6.69267117248217E+02
i= 3, j= 4, k(i,j)=-1.31596353379190E+03
i= 3, j= 5, k(i,j)= 1.56792969496315E+03
i= 3, j= 6, k(i,j)=-1.86251355848503E+03
i= 3, j= 7, k(i,j)= 2.84482204629459E+03
i= 3, j= 8, k(i,j)=-7.26558108834729E+03
i= 3, j= 9, k(i,j)= 3.38379797032462E+04
i= 3, j= 10, k(i,j)=-3.53109234445447E+05
i= 4, j= 1, k(i,j)= 9.50973662673217E+04
i= 4, j= 2, k(i,j)=-6.03338594020673E+03
i= 4, j= 3, k(i,j)=-1.15883671986035E+02
i= 4, j= 4, k(i,j)= 1.25824614385365E+03
i= 4, j= 5, k(i,j)=-1.69866349492619E+03
i= 4, j= 6, k(i,j)= 1.89161031911898E+03
i= 4, j= 7, k(i,j)=-2.37903449004793E+03
i= 4, j= 8, k(i,j)= 5.22161107554986E+03
i= 4, j= 9, k(i,j)=-2.37197979025678E+04
i= 4, j= 10, k(i,j)= 2.50590118177996E+05
i= 5, j= 1, k(i,j)= 6.43126997408476E+04
i= 5, j= 2, k(i,j)=-6.37129119733847E+03
i= 5, j= 3, k(i,j)= 1.96663015392987E+03
i= 5, j= 4, k(i,j)=-1.65737222132017E+03
i= 5, j= 5, k(i,j)= 1.80978454375097E+03
i= 5, j= 6, k(i,j)=-1.67632041382590E+03
i= 5, j= 7, k(i,j)= 1.19743706236327E+03
i= 5, j= 8, k(i,j)=-5.26169560192861E+02
i= 5, j= 9, k(i,j)=-1.19953262991661E+03
i= 5, j= 10, k(i,j)= 2.26281439561120E+04
i= 6, j= 1, k(i,j)=-7.92400633411781E+04
i= 6, j= 2, k(i,j)= 7.77091957427418E+03
i= 6, j= 3, k(i,j)=-2.18187135999970E+03
i= 6, j= 4, k(i,j)= 1.65590662953312E+03
i= 6, j= 5, k(i,j)=-1.81498580813220E+03
i= 6, j= 6, k(i,j)= 1.77755420197826E+03
i= 6, j= 7, k(i,j)=-1.35374271227488E+03
i= 6, j= 8, k(i,j)= 6.73104353330301E+02
i= 6, j= 9, k(i,j)= 1.14935209779023E+03
i= 6, j= 10, k(i,j)=-2.44937260924500E+04
i= 7, j= 1, k(i,j)=-4.23242635813591E+05
i= 7, j= 2, k(i,j)= 3.88940764757233E+04
i= 7, j= 3, k(i,j)=-7.36743113837517E+03
i= 7, j= 4, k(i,j)= 1.70226965964489E+03
i= 7, j= 5, k(i,j)= 4.70574415095442E+01
i= 7, j= 6, k(i,j)=-7.30015333796070E+02
i= 7, j= 7, k(i,j)= 1.11350160746218E+03
i= 7, j= 8, k(i,j)=-2.83753768072063E+03
i= 7, j= 9, k(i,j)= 1.71150448968844E+04
i= 7, j= 10, k(i,j)=-2.23577390711452E+05
i= 8, j= 1, k(i,j)= 9.62336735131987E+05
i= 8, j= 2, k(i,j)=-9.15909639563218E+04
i= 8, j= 3, k(i,j)= 1.89082016264388E+04
i= 8, j= 4, k(i,j)=-6.14992942551793E+03
i= 8, j= 5, k(i,j)= 2.65145727246950E+03
i= 8, j= 6, k(i,j)=-1.46460988232292E+03
i= 8, j= 7, k(i,j)= 1.01346173139035E+03
i= 8, j= 8, k(i,j)= 4.07397498357274E+02
i= 8, j= 9, k(i,j)=-1.54361078679408E+04
i= 8, j= 10, k(i,j)= 2.74747655154431E+05
i= 9, j= 1, k(i,j)=-3.54252325465138E+04
i= 9, j= 2, k(i,j)= 3.40747724996364E+03
i= 9, j= 3, k(i,j)=-6.64749859244103E+02
i= 9, j= 4, k(i,j)= 1.06508160863423E+02
i= 9, j= 5, k(i,j)= 1.18042006245139E+02
i= 9, j= 6, k(i,j)=-2.07316923215356E+02
i= 9, j= 7, k(i,j)= 1.77906430868851E+02
i= 9, j= 8, k(i,j)=-9.88859505192805E+01
i= 9, j= 9, k(i,j)= 2.45471724565266E+02
i= 9, j= 10, k(i,j)=-5.89916159914564E+03
i= 10, j= 1, k(i,j)= 0.00000000000000E+00
i= 10, j= 2, k(i,j)= 0.00000000000000E+00
i= 10, j= 3, k(i,j)= 0.00000000000000E+00
i= 10, j= 4, k(i,j)= 0.00000000000000E+00
i= 10, j= 5, k(i,j)= 0.00000000000000E+00
i= 10, j= 6, k(i,j)= 0.00000000000000E+00
i= 10, j= 7, k(i,j)= 0.00000000000000E+00
i= 10, j= 8, k(i,j)= 0.00000000000000E+00
i= 10, j= 9, k(i,j)= 0.00000000000000E+00
i= 10, j= 10, k(i,j)= 1.00000000000000E+00

f computed forcing function 
f( 1)= 2.00000000000000E+00
f( 2)=-3.51361607142845E-01
f( 3)=-2.41071428571476E-02
f( 4)=-4.31785714285709E-01
f( 5)=-1.28973214285717E-01
f( 6)=-1.28973214285715E-01
f( 7)=-4.31785714285710E-01
f( 8)=-2.41071428571480E-02
f( 9)=-3.51361607142845E-01
f( 10)= 5.00000000000000E+00

u computed Galerkin, Ua analytic, error 
u( 1)=  2.00000, Ua=  2.00000, err=  0.00000
u( 2)= 32.67743, Ua=  2.23457, err= 30.44286
u( 3)= 49.86483, Ua=  2.49383, err= 47.37101
u( 4)= 53.43246, Ua=  2.77778, err= 50.65468
u( 5)= 50.26635, Ua=  3.08642, err= 47.17993
u( 6)= 58.26447, Ua=  3.41975, err= 54.84472
u( 7)= 89.86206, Ua=  3.77778, err= 86.08428
u( 8)=110.62541, Ua=  4.16049, err=106.46492
u( 9)= 71.50689, Ua=  4.56790, err= 66.93899
u( 10)=  5.00000, Ua=  5.00000, err=  0.00000
                   maxerr= 1.06464919318448E+02, avgerr= 4.89981382439149E+01