fem_check21a_tri.c running 
Given 3 ux + 2 uy + u = 2 x + 3 y + 13 
Analytic solution u(x,y) =  1 + 2 x + 3 y 
triquad ready for integration over triangles
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
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_int1a running with np=3, nv=9
integral=0.35416666666666585, at i=6, j=6
intg fg =0.42708333333333226, at i=6
integral=-0.23958333333333276, at i=1, j=6
integral=-0.07291666666666649, at i=4, j=6
finished k=0
computing local stiffness matrix for triangle 1
nodes i1=1, i2=6, i3=8
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_int1a running with np=3, nv=9
integral=0.3749999999999992, at i=6, j=6
intg fg =0.8124999999999986, at i=6
integral=-0.3958333333333326, at i=1, j=6
integral=0.10416666666666648, at i=8, j=6
finished k=1
computing local stiffness matrix for triangle 2
nodes i1=2, i2=9, i3=5
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_int1a running with np=3, nv=9
integral=-0.645833333333332, at i=5, j=5
intg fg =0.614583333333332, at i=5
integral=0.4270833333333324, at i=2, j=5
integral=0.26041666666666613, at i=9, j=5
finished k=2
computing local stiffness matrix for triangle 3
nodes i1=4, i2=2, i3=5
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_int1a running with np=3, nv=9
integral=0.35416666666666596, at i=5, j=5
intg fg =0.5937499999999988, at i=5
integral=-0.23958333333333282, at i=4, j=5
integral=-0.07291666666666652, at i=2, j=5
finished k=3
computing local stiffness matrix for triangle 4
nodes i1=6, i2=4, i3=5
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_int1a running with np=3, nv=9
integral=0.10416666666666644, at i=6, j=6
intg fg =0.4947916666666657, at i=6
integral=-0.3229166666666661, at i=4, j=6
integral=0.2604166666666662, at i=5, j=6
integral=0.2708333333333327, at i=5, j=5
intg fg =0.5364583333333321, at i=5
integral=0.09374999999999979, at i=6, j=5
integral=-0.32291666666666596, at i=4, j=5
finished k=4
computing local stiffness matrix for triangle 5
nodes i1=6, i2=5, i3=0
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_int1a running with np=3, nv=9
integral=-0.22916666666666619, at i=6, j=6
intg fg =0.5052083333333324, at i=6
integral=-0.0729166666666665, at i=5, j=6
integral=0.3437499999999994, at i=0, j=6
integral=-0.062499999999999896, at i=5, j=5
intg fg =0.5468749999999989, at i=5
integral=-0.23958333333333284, at i=6, j=5
integral=0.3437499999999994, at i=0, j=5
integral=0.35416666666666585, at i=0, j=0
intg fg =0.5312499999999989, at i=0
integral=-0.23958333333333282, at i=6, j=0
integral=-0.0729166666666665, at i=5, j=0
finished k=5
computing local stiffness matrix for triangle 6
nodes i1=6, i2=0, i3=7
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_int1a running with np=3, nv=9
integral=-0.3749999999999992, at i=6, j=6
intg fg =0.9687499999999981, at i=6
integral=0.354166666666666, at i=0, j=6
integral=0.10416666666666644, at i=7, j=6
integral=0.3749999999999993, at i=0, j=0
intg fg =1.0208333333333315, at i=0
integral=-0.3958333333333326, at i=6, j=0
integral=0.10416666666666648, at i=7, j=0
integral=0.12499999999999971, at i=7, j=7
intg fg =1.0104166666666645, at i=7
integral=-0.3958333333333324, at i=6, j=7
integral=0.35416666666666585, at i=0, j=7
finished k=6
computing local stiffness matrix for triangle 7
nodes i1=8, i2=6, i3=7
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_int1a running with np=3, nv=9
integral=-0.0416666666666666, at i=6, j=6
intg fg =0.9062499999999984, at i=6
integral=-0.3124999999999994, at i=8, j=6
integral=0.4374999999999992, at i=7, j=6
integral=0.45833333333333226, at i=7, j=7
intg fg =0.9479166666666645, at i=7
integral=-0.31249999999999933, at i=8, j=7
integral=-0.06249999999999984, at i=6, j=7
finished k=7
computing local stiffness matrix for triangle 8
nodes i1=8, i2=7, i3=3
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_int1a running with np=3, nv=9
integral=0.3749999999999992, at i=7, j=7
intg fg =0.9791666666666647, at i=7
integral=-0.3958333333333326, at i=8, j=7
integral=0.10416666666666648, at i=3, j=7
finished k=8
computing local stiffness matrix for triangle 9
nodes i1=9, i2=3, i3=7
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_int1a running with np=3, nv=9
integral=-0.645833333333332, at i=7, j=7
intg fg =0.5312499999999989, at i=7
integral=0.4270833333333324, at i=9, j=7
integral=0.26041666666666613, at i=3, j=7
finished k=9
computing local stiffness matrix for triangle 10
nodes i1=5, i2=9, i3=7
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_int1a running with np=3, nv=9
integral=-0.2291666666666662, at i=5, j=5
intg fg =0.5781249999999989, at i=5
integral=0.6770833333333319, at i=9, j=5
integral=-0.4062499999999992, at i=7, j=5
integral=-0.3958333333333325, at i=7, j=7
intg fg =0.5572916666666655, at i=7
integral=-0.23958333333333282, at i=5, j=7
integral=0.6770833333333319, at i=9, j=7
finished k=10
computing local stiffness matrix for triangle 11
nodes i1=5, i2=7, i3=0
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_int1a running with np=3, nv=9
integral=0.43749999999999906, at i=5, j=5
intg fg =0.5677083333333321, at i=5
integral=0.2604166666666662, at i=7, j=5
integral=-0.6562499999999987, at i=0, j=5
integral=0.2708333333333328, at i=7, j=7
intg fg =0.546874999999999, at i=7
integral=0.4270833333333326, at i=5, j=7
integral=-0.6562499999999987, at i=0, j=7
integral=-0.6458333333333319, at i=0, j=0
intg fg =0.5520833333333321, at i=0
integral=0.42708333333333237, at i=5, j=0
integral=0.2604166666666661, 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)=0.08333333333333326
K(0,1)=0.0
K(0,2)=0.0
K(0,3)=0.0
K(0,4)=0.0
K(0,5)=0.35416666666666585
K(0,6)=-0.6354166666666654
K(0,7)=0.36458333333333254
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)=-0.3124999999999993
K(5,1)=0.0
K(5,2)=0.3541666666666659
K(5,3)=0.0
K(5,4)=-0.5624999999999988
K(5,5)=0.12499999999999961
K(5,6)=-0.14583333333333304
K(5,7)=-0.14583333333333304
K(5,8)=0.0
K(5,9)=0.937499999999998
K(6,0)=0.6979166666666654
K(6,1)=-0.6354166666666654
K(6,2)=0.0
K(6,3)=0.0
K(6,4)=-0.3958333333333326
K(6,5)=0.18749999999999967
K(6,6)=0.18749999999999947
K(6,7)=0.5416666666666656
K(6,8)=-0.20833333333333293
K(6,9)=0.0
K(7,0)=-0.3020833333333328
K(7,1)=0.0
K(7,2)=0.0
K(7,3)=0.3645833333333326
K(7,4)=0.0
K(7,5)=0.18749999999999978
K(7,6)=-0.45833333333333226
K(7,7)=0.18749999999999944
K(7,8)=-0.7083333333333319
K(7,9)=1.1041666666666643
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)=2.1041666666666625, 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)=3.437499999999993, ug[5]=0.0
F(6)=4.114583333333325, ug[6]=0.0
F(7)=4.572916666666657, 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]=1.0000000000000009, Ua=1.0, err=8.881784197001252E-16
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]=2.5, Ua=2.5, err=0.0
ug[6]=-1.5, Ua=-1.5, err=0.0
ug[7]=0.4999999999999982, Ua=0.5, err=-1.7763568394002505E-15
ug[8]=-2.0, Ua=-2.0, err=0.0
ug[9]=2.0, Ua=2.0, err=0.0
                 maxerr=1.7763568394002505E-15, avgerr=2.6645352591003756E-16