fem_check21_tri.c running 
Given 3 ux + 2 uy + u = 2 x + 3 y + 13 
Analytic solution u(x,y) =  1 + 2 x + 3 y 
about to read triangles from 22_ts.tri
1 4 6 
index=0, last=1
index=2, last=3
index=4, last=5
tri 0 has vertices 1  4  6
1 6 8 
index=0, last=1
index=2, last=3
index=4, last=5
tri 1 has vertices 1  6  8
2 9 5 
index=0, last=1
index=2, last=3
index=4, last=5
tri 2 has vertices 2  9  5
4 2 5 
index=0, last=1
index=2, last=3
index=4, last=5
tri 3 has vertices 4  2  5
6 4 5 
index=0, last=1
index=2, last=3
index=4, last=5
tri 4 has vertices 6  4  5
6 5 0 
index=0, last=1
index=2, last=3
index=4, last=5
tri 5 has vertices 6  5  0
6 0 7 
index=0, last=1
index=2, last=3
index=4, last=5
tri 6 has vertices 6  0  7
8 6 7 
index=0, last=1
index=2, last=3
index=4, last=5
tri 7 has vertices 8  6  7
8 7 3 
index=0, last=1
index=2, last=3
index=4, last=5
tri 8 has vertices 8  7  3
9 3 7 
index=0, last=1
index=2, last=3
index=4, last=5
tri 9 has vertices 9  3  7
5 9 7 
index=0, last=1
index=2, last=3
index=4, last=5
tri 10 has vertices 5  9  7
5 7 0 
index=0, last=1
index=2, last=3
index=4, last=5
tri 11 has vertices 5  7  0
12 triangles read from 22_ts.tri
subtracting minvert=0 from all vertices, using base zero
finding unique of nold=36
found unique of n=10
about to read boundary from 22_ts.bound
1 4 
index=0, last=1
index=2, last=3
boundary segment nbound=0 has vertices 1, 4
2 9 
index=0, last=1
index=2, last=3
boundary segment nbound=1 has vertices 2, 9
3 8 
index=0, last=1
index=2, last=3
boundary segment nbound=2 has vertices 3, 8
4 2 
index=0, last=1
index=2, last=3
boundary segment nbound=3 has vertices 4, 2
8 1 
index=0, last=1
index=2, last=3
boundary segment nbound=4 has vertices 8, 1
9 3 
index=0, last=1
index=2, last=3
boundary segment nbound=5 has vertices 9, 3
read Dirichlet boundaries from 22_ts.bound
subtracting minvert=0 from all vertices, using base zero
finding unique of nold=12
found unique of n=6
freevert na=10, nb=6
freevert nc free = 4
unique boundary 1
unique boundary 2
unique boundary 3
unique boundary 4
unique boundary 8
unique boundary 9
number of free vertices is 4
free vertex 0
free vertex 5
free vertex 6
free vertex 7
about to read coordinates from 22_ts.coord
0.000000 0.000000 
index=0, last=8
index=9, last=17
coordinate 0 at  0.0, 0.0
-1.000000 -1.000000 
index=0, last=9
index=10, last=19
coordinate 1 at  -1.0, -1.0
0.000000 1.000000 
index=0, last=8
index=9, last=17
coordinate 2 at  0.0, 1.0
1.000000 -1.000000 
index=0, last=8
index=9, last=18
coordinate 3 at  1.0, -1.0
-0.500000 0.000000 
index=0, last=9
index=10, last=18
coordinate 4 at  -0.5, 0.0
0.000000 0.500000 
index=0, last=8
index=9, last=17
coordinate 5 at  0.0, 0.5
-0.500000 -0.500000 
index=0, last=9
index=10, last=19
coordinate 6 at  -0.5, -0.5
0.500000 -0.500000 
index=0, last=8
index=9, last=18
coordinate 7 at  0.5, -0.5
0.000000 -1.000000 
index=0, last=8
index=9, last=18
coordinate 8 at  0.0, -1.0
0.500000 0.000000 
index=0, last=8
index=9, last=17
coordinate 9 at  0.5, 0.0
coordinates read from 22_ts.coord
xmin=-1.0, xmax=1.0, ymin=-1.0, ymax=1.0
nvert=10, nbound=6, nuniqueb=6, nfree=4, ntri=12
compute global stiffness matrix 
computing local stiffness matrix for triangle 0
nodes i1=1, i2=4, i3=6, area=0.125
coord (-1.0,-1.0) (-0.5,0.0) (-0.5,-0.5) 
cm matrix  of  am cm = ym   solve for cm 
 -1.0 -2.0 -0.0
cm matrix  of  am cm = ym   solve for cm 
 0.0 -2.0 2.0
cm matrix  of  am cm = ym   solve for cm 
 2.0 4.0 -2.0
tri_int1 running with np=30, nv=496
integral=0.35401063453158965, at i=6, j=6
intg fg =0.42700531726579505, at i=6
integral=-0.2395053172657953, at i=1, j=6
integral=-0.0728386505991285, at i=4, j=6
finished k=0
computing local stiffness matrix for triangle 1
nodes i1=1, i2=6, i3=8, area=0.25
coord (-1.0,-1.0) (-0.5,-0.5) (0.0,-1.0) 
cm matrix  of  am cm = ym   solve for cm 
 -1.0 -1.0 -1.0
cm matrix  of  am cm = ym   solve for cm 
 2.0 0.0 2.0
cm matrix  of  am cm = ym   solve for cm 
 0.0 1.0 -1.0
tri_int1 running with np=30, nv=496
integral=0.37468793572984777, at i=6, j=6
intg fg =0.8120319035947708, at i=6
integral=-0.39567730119825695, at i=1, j=6
integral=0.10432269880174287, at i=8, j=6
finished k=1
computing local stiffness matrix for triangle 2
nodes i1=2, i2=9, i3=5, area=0.125
coord (0.0,1.0) (0.5,0.0) (0.0,0.5) 
cm matrix  of  am cm = ym   solve for cm 
 -1.0 2.0 2.0
cm matrix  of  am cm = ym   solve for cm 
 0.0 2.0 0.0
cm matrix  of  am cm = ym   solve for cm 
 2.0 -4.0 -2.0
tri_int1 running with np=30, nv=496
integral=-0.6459893654684109, at i=5, j=5
intg fg =0.6146613494008721, at i=5
integral=0.4271613494008718, at i=2, j=5
integral=0.2604946827342049, at i=9, j=5
finished k=2
computing local stiffness matrix for triangle 3
nodes i1=4, i2=2, i3=5, area=0.125
coord (-0.5,0.0) (0.0,1.0) (0.0,0.5) 
cm matrix  of  am cm = ym   solve for cm 
 0.0 -2.0 -0.0
cm matrix  of  am cm = ym   solve for cm 
 -1.0 -2.0 2.0
cm matrix  of  am cm = ym   solve for cm 
 2.0 4.0 -2.0
tri_int1 running with np=30, nv=496
integral=0.35401063453158954, at i=5, j=5
intg fg =0.5936719839324629, at i=5
integral=-0.23950531726579527, at i=4, j=5
integral=-0.07283865059912847, at i=2, j=5
finished k=3
computing local stiffness matrix for triangle 4
nodes i1=6, i2=4, i3=5, area=0.125
coord (-0.5,-0.5) (-0.5,0.0) (0.0,0.5) 
cm matrix  of  am cm = ym   solve for cm 
 1.0 2.0 -2.0
cm matrix  of  am cm = ym   solve for cm 
 -1.0 -4.0 2.0
cm matrix  of  am cm = ym   solve for cm 
 1.0 2.0 0.0
tri_int1 running with np=30, nv=496
integral=0.1040106345315905, at i=6, j=6
intg fg =0.4952207550381262, at i=6
integral=-0.32283865059912853, at i=4, j=6
integral=0.260494682734205, at i=5, j=6
integral=0.2706773011982574, at i=5, j=5
intg fg =0.5359512288943347, at i=5
integral=0.09382801606753817, at i=6, j=5
integral=-0.3228386505991286, at i=4, j=5
finished k=4
computing local stiffness matrix for triangle 5
nodes i1=6, i2=5, i3=0, area=0.125
coord (-0.5,-0.5) (0.0,0.5) (0.0,0.0) 
cm matrix  of  am cm = ym   solve for cm 
 0.0 -2.0 -0.0
cm matrix  of  am cm = ym   solve for cm 
 0.0 -2.0 2.0
cm matrix  of  am cm = ym   solve for cm 
 1.0 4.0 -2.0
tri_int1 running with np=30, nv=496
integral=-0.2293226988017428, at i=6, j=6
intg fg =0.5057154377723315, at i=6
integral=-0.07283865059912852, at i=5, j=6
integral=0.3438280160675378, at i=0, j=6
integral=-0.06265603213507628, at i=5, j=5
intg fg =0.5464459116285404, at i=5
integral=-0.23950531726579538, at i=6, j=5
integral=0.34382801606753816, at i=0, j=5
integral=0.3540106345315894, at i=0, j=0
intg fg =0.531171983932462, at i=0
integral=-0.2395053172657952, at i=6, j=0
integral=-0.07283865059912849, at i=5, j=0
finished k=5
computing local stiffness matrix for triangle 6
nodes i1=6, i2=0, i3=7, area=0.25
coord (-0.5,-0.5) (0.0,0.0) (0.5,-0.5) 
cm matrix  of  am cm = ym   solve for cm 
 0.0 -1.0 -1.0
cm matrix  of  am cm = ym   solve for cm 
 1.0 0.0 2.0
cm matrix  of  am cm = ym   solve for cm 
 0.0 1.0 -1.0
tri_int1 running with np=30, nv=496
integral=-0.3753120642701535, at i=6, j=6
intg fg =0.9694521446078425, at i=6
integral=0.35432269880174266, at i=0, j=6
integral=0.10432269880174284, at i=7, j=6
integral=0.37468793572984777, at i=0, j=0
intg fg =1.0203652369281049, at i=0
integral=-0.39567730119825717, at i=6, j=0
integral=0.10432269880174289, at i=7, j=0
integral=0.12468793572984727, at i=7, j=7
intg fg =1.0101826184640514, at i=7
integral=-0.3956773011982574, at i=6, j=7
integral=0.3543226988017426, at i=0, j=7
finished k=6
computing local stiffness matrix for triangle 7
nodes i1=8, i2=6, i3=7, area=0.25
coord (0.0,-1.0) (-0.5,-0.5) (0.5,-0.5) 
cm matrix  of  am cm = ym   solve for cm 
 -1.0 0.0 -2.0
cm matrix  of  am cm = ym   solve for cm 
 1.0 -1.0 1.0
cm matrix  of  am cm = ym   solve for cm 
 1.0 1.0 1.0
tri_int1 running with np=30, nv=496
integral=-0.041978730936819066, at i=6, j=6
intg fg =0.9064840482026137, at i=6
integral=-0.3123439678649241, at i=8, j=6
integral=0.4376560321350762, at i=7, j=6
integral=0.458021269063181, at i=7, j=7
intg fg =0.9472145220588232, at i=7
integral=-0.31234396786492397, at i=8, j=7
integral=-0.06234396786492376, at i=6, j=7
finished k=7
computing local stiffness matrix for triangle 8
nodes i1=8, i2=7, i3=3, area=0.25
coord (0.0,-1.0) (0.5,-0.5) (1.0,-1.0) 
cm matrix  of  am cm = ym   solve for cm 
 0.0 -1.0 -1.0
cm matrix  of  am cm = ym   solve for cm 
 2.0 0.0 2.0
cm matrix  of  am cm = ym   solve for cm 
 -1.0 1.0 -1.0
tri_int1 running with np=30, nv=496
integral=0.37468793572984777, at i=7, j=7
intg fg =0.9786985702614374, at i=7
integral=-0.39567730119825695, at i=8, j=7
integral=0.10432269880174287, at i=3, j=7
finished k=8
computing local stiffness matrix for triangle 9
nodes i1=9, i2=3, i3=7, area=0.125
coord (0.5,0.0) (1.0,-1.0) (0.5,-0.5) 
cm matrix  of  am cm = ym   solve for cm 
 0.0 2.0 2.0
cm matrix  of  am cm = ym   solve for cm 
 -1.0 2.0 0.0
cm matrix  of  am cm = ym   solve for cm 
 2.0 -4.0 -2.0
tri_int1 running with np=30, nv=496
integral=-0.6459893654684111, at i=7, j=7
intg fg =0.531328016067539, at i=7
integral=0.4271613494008721, at i=9, j=7
integral=0.26049468273420495, at i=3, j=7
finished k=9
computing local stiffness matrix for triangle 10
nodes i1=5, i2=9, i3=7, area=0.125
coord (0.0,0.5) (0.5,0.0) (0.5,-0.5) 
cm matrix  of  am cm = ym   solve for cm 
 1.0 -2.0 -0.0
cm matrix  of  am cm = ym   solve for cm 
 -1.0 4.0 2.0
cm matrix  of  am cm = ym   solve for cm 
 1.0 -2.0 -2.0
tri_int1 running with np=30, nv=496
integral=-0.22932269880174305, at i=5, j=5
intg fg =0.5779299598311549, at i=5
integral=0.6771613494008721, at i=9, j=5
integral=-0.40617198393246207, at i=7, j=5
integral=-0.39598936546841024, at i=7, j=7
intg fg =0.5575647229030503, at i=7
integral=-0.23950531726579521, at i=5, j=7
integral=0.677161349400872, at i=9, j=7
finished k=10
computing local stiffness matrix for triangle 11
nodes i1=5, i2=7, i3=0, area=0.125
coord (0.0,0.5) (0.5,-0.5) (0.0,0.0) 
cm matrix  of  am cm = ym   solve for cm 
 0.0 2.0 2.0
cm matrix  of  am cm = ym   solve for cm 
 0.0 2.0 0.0
cm matrix  of  am cm = ym   solve for cm 
 1.0 -4.0 -2.0
tri_int1 running with np=30, nv=496
integral=0.4373439678649244, at i=5, j=5
intg fg =0.5674352770969499, at i=5
integral=0.26049468273420495, at i=7, j=5
integral=-0.6561719839324616, at i=0, j=5
integral=0.2706773011982581, at i=7, j=7
intg fg =0.5470700401688454, at i=7
integral=0.42716134940087147, at i=5, j=7
integral=-0.6561719839324618, at i=0, j=7
integral=-0.6459893654684109, at i=0, j=0
intg fg =0.5521613494008709, at i=0
integral=0.4271613494008719, at i=5, j=0
integral=0.26049468273420484, at i=7, j=0
finished k=11
tri 0 has vertices 1, 4, 6
tri 1 has vertices 1, 6, 8
tri 2 has vertices 2, 9, 5
tri 3 has vertices 4, 2, 5
tri 4 has vertices 6, 4, 5
tri 5 has vertices 6, 5, 0
tri 6 has vertices 6, 0, 7
tri 7 has vertices 8, 6, 7
tri 8 has vertices 8, 7, 3
tri 9 has vertices 9, 3, 7
tri 10 has vertices 5, 9, 7
tri 11 has vertices 5, 7, 0
vertices, coordinates and analytic values 
coordinate 0 at 0.0, 0.0, uana=1.0
coordinate 1 at -1.0, -1.0, uana=-4.0
coordinate 2 at 0.0, 1.0, uana=4.0
coordinate 3 at 1.0, -1.0, uana=0.0
coordinate 4 at -0.5, 0.0, uana=0.0
coordinate 5 at 0.0, 0.5, uana=2.5
coordinate 6 at -0.5, -0.5, uana=-1.5
coordinate 7 at 0.5, -0.5, uana=0.5
coordinate 8 at 0.0, -1.0, uana=-2.0
coordinate 9 at 0.5, 0.0, uana=2.0
k computed stiffness matrix, if debug 
K(0,0)=0.08270920479302624
K(0,1)=0.0
K(0,2)=0.0
K(0,3)=0.0
K(0,4)=0.0
K(0,5)=0.35432269880174344
K(0,6)=-0.6351826184640523
K(0,7)=0.3648173815359477
K(0,8)=0.0
K(0,9)=0.0
K(1,0)=0.0
K(1,1)=1.0
K(1,2)=0.0
K(1,3)=0.0
K(1,4)=0.0
K(1,5)=0.0
K(1,6)=0.0
K(1,7)=0.0
K(1,8)=0.0
K(1,9)=0.0
K(2,0)=0.0
K(2,1)=0.0
K(2,2)=1.0
K(2,3)=0.0
K(2,4)=0.0
K(2,5)=0.0
K(2,6)=0.0
K(2,7)=0.0
K(2,8)=0.0
K(2,9)=0.0
K(3,0)=0.0
K(3,1)=0.0
K(3,2)=0.0
K(3,3)=1.0
K(3,4)=0.0
K(3,5)=0.0
K(3,6)=0.0
K(3,7)=0.0
K(3,8)=0.0
K(3,9)=0.0
K(4,0)=0.0
K(4,1)=0.0
K(4,2)=0.0
K(4,3)=0.0
K(4,4)=1.0
K(4,5)=0.0
K(4,6)=0.0
K(4,7)=0.0
K(4,8)=0.0
K(4,9)=0.0
K(5,0)=-0.3123439678649234
K(5,1)=0.0
K(5,2)=0.35432269880174333
K(5,3)=0.0
K(5,4)=-0.5623439678649238
K(5,5)=0.12406380718954108
K(5,6)=-0.14567730119825723
K(5,7)=-0.14567730119825711
K(5,8)=0.0
K(5,9)=0.9376560321350771
K(6,0)=0.6981507148692805
K(6,1)=-0.6351826184640522
K(6,2)=0.0
K(6,3)=0.0
K(6,4)=-0.39567730119825706
K(6,5)=0.18765603213507648
K(6,6)=0.1860957107843126
K(6,7)=0.541978730936819
K(6,8)=-0.2080212690631812
K(6,9)=0.0
K(7,0)=-0.3018492851307192
K(7,1)=0.0
K(7,2)=0.0
K(7,3)=0.36481738153594784
K(7,4)=0.0
K(7,5)=0.18765603213507626
K(7,6)=-0.45802126906318114
K(7,7)=0.1860957107843128
K(7,8)=-0.7080212690631809
K(7,9)=1.104322698801744
K(8,0)=0.0
K(8,1)=0.0
K(8,2)=0.0
K(8,3)=0.0
K(8,4)=0.0
K(8,5)=0.0
K(8,6)=0.0
K(8,7)=0.0
K(8,8)=1.0
K(8,9)=0.0
K(9,0)=0.0
K(9,1)=0.0
K(9,2)=0.0
K(9,3)=0.0
K(9,4)=0.0
K(9,5)=0.0
K(9,6)=0.0
K(9,7)=0.0
K(9,8)=0.0
K(9,9)=1.0
f computed forcing function and boundary, if debug 
F(0)=2.1036985702614377, ug[0]=0.0
F(1)=-4.0, ug[1]=0.0
F(2)=4.0, ug[2]=0.0
F(3)=0.0, ug[3]=0.0
F(4)=0.0, ug[4]=0.0
F(5)=3.4360957107843153, ug[5]=0.0
F(6)=4.11590960648148, ug[6]=0.0
F(7)=4.572058489923747, ug[7]=0.0
F(8)=-2.0, ug[8]=0.0
F(9)=2.0, ug[9]=0.0
ug computed Galerkin, Ua analytic, error 
ug[0]=1.0000000000000089, Ua=1.0, err=8.881784197001252E-15
ug[1]=-4.0, Ua=-4.0, err=0.0
ug[2]=4.0, Ua=4.0, err=0.0
ug[3]=0.0, Ua=0.0, err=0.0
ug[4]=0.0, Ua=0.0, err=0.0
ug[5]=2.5000000000000036, Ua=2.5, err=3.552713678800501E-15
ug[6]=-1.5000000000000089, Ua=-1.5, err=-8.881784197001252E-15
ug[7]=0.4999999999999831, Ua=0.5, err=-1.687538997430238E-14
ug[8]=-2.0, Ua=-2.0, err=0.0
ug[9]=2.0, Ua=2.0, err=0.0
                 maxerr=1.687538997430238E-14, avgerr=3.819167204710538E-15