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 C.tri triangles read from C.tri tri 0 has vertices 9 15 4 tri 1 has vertices 11 6 10 tri 2 has vertices 15 9 10 tri 3 has vertices 8 9 4 tri 4 has vertices 9 8 7 tri 5 has vertices 8 1 7 tri 6 has vertices 7 5 9 tri 7 has vertices 10 9 5 tri 8 has vertices 11 12 3 tri 9 has vertices 6 13 15 tri 10 has vertices 10 12 11 tri 11 has vertices 12 10 5 tri 12 has vertices 13 2 14 tri 13 has vertices 14 15 13 tri 14 has vertices 15 10 6 tri 15 has vertices 14 4 15 subtracting minvert=1 from all vertices, using base zero finding unique of nold=48 found unique of n=15 about to read boundary from C.bound Dirichlet boundaries from C.bound boundary segment 0 has vertices 1 8 boundary segment 1 has vertices 2 13 boundary segment 2 has vertices 3 12 boundary segment 3 has vertices 4 14 boundary segment 4 has vertices 5 7 boundary segment 5 has vertices 6 11 boundary segment 6 has vertices 7 1 boundary segment 7 has vertices 8 4 boundary segment 8 has vertices 11 3 boundary segment 9 has vertices 12 5 boundary segment 10 has vertices 13 6 boundary segment 11 has vertices 14 2 subtracting minvert=1 from all vertices, using base zero finding unique of nold=24 found unique of n=12 freevert na=15, nb=12 freevert nc free = 3 number of free vertices is 3 free vertex 8 free vertex 9 free vertex 14 about to read coordinates from C.coord coordinates read from C.coord coordinate 0 at 0.00 , 0.00 coordinate 1 at 0.50 , 0.87 coordinate 2 at 1.00 , 0.00 coordinate 3 at 0.25 , 0.43 coordinate 4 at 0.50 , 0.00 coordinate 5 at 0.75 , 0.43 coordinate 6 at 0.25 , 0.00 coordinate 7 at 0.13 , 0.22 coordinate 8 at 0.37 , 0.22 coordinate 9 at 0.62 , 0.22 coordinate 10 at 0.87 , 0.22 coordinate 11 at 0.75 , 0.00 coordinate 12 at 0.63 , 0.65 coordinate 13 at 0.37 , 0.65 coordinate 14 at 0.50 , 0.43 xmin=0, xmax=1, ymin=0, ymax=0.866 nvert=15, nbound=12, nfree=3, ntri=16 compute global stiffness matrix computing local stiffness matrix for triangle 0 nodes i1=8, i2=14, i3=3, area=0.027060 coord (0.374989,0.216497) (0.499975,0.432989) (0.249994,0.432990) cm matrix of am cm = ym solve for cm 2.00 -0.00 -4.62 cm matrix of am cm = ym solve for cm -2.00 4.00 2.31 cm matrix of am cm = ym solve for cm 1.00 -4.00 2.31 tri_int1 running with np=30, nv=496 integral=-0.078852, at i=8, j=8 intg fg =0.132832, at i=8 integral=0.152184, at i=14, j=8 integral=-0.064312, at i=3, j=8 integral=0.154388, at i=14, j=14 intg fg =0.134815, at i=14 integral=-0.081056, at i=8, j=14 integral=-0.064312, at i=3, j=14 finished k=0 computing local stiffness matrix for triangle 1 nodes i1=10, i2=5, i3=9, area=0.027064 coord (0.874997,0.216505) (0.749994,0.433010) (0.624986,0.216511) cm matrix of am cm = ym solve for cm -2.00 4.00 -2.31 cm matrix of am cm = ym solve for cm -1.00 0.00 4.62 cm matrix of am cm = ym solve for cm 4.00 -4.00 -2.31 tri_int1 running with np=30, nv=496 integral=-0.145443, at i=9, j=9 intg fg =0.137593, at i=9 integral=0.068852, at i=10, j=9 integral=0.085612, at i=5, j=9 finished k=1 computing local stiffness matrix for triangle 2 nodes i1=14, i2=8, i3=9, area=0.027060 coord (0.499975,0.432989) (0.374989,0.216497) (0.624986,0.216511) cm matrix of am cm = ym solve for cm -1.00 -0.00 4.62 cm matrix of am cm = ym solve for cm 3.00 -4.00 -2.31 cm matrix of am cm = ym solve for cm -1.00 4.00 -2.31 tri_int1 running with np=30, nv=496 integral=0.087802, at i=14, j=14 intg fg =0.135047, at i=14 integral=-0.147637, at i=8, j=14 integral=0.068856, at i=9, j=14 integral=-0.145433, at i=8, j=8 intg fg =0.133064, at i=8 integral=0.085597, at i=14, j=8 integral=0.068856, at i=9, j=8 integral=0.071060, at i=9, j=9 intg fg =0.134167, at i=9 integral=0.085597, at i=14, j=9 integral=-0.147637, at i=8, j=9 finished k=2 computing local stiffness matrix for triangle 3 nodes i1=7, i2=8, i3=3, area=0.027060 coord (0.125003,0.216505) (0.374989,0.216497) (0.249994,0.432990) cm matrix of am cm = ym solve for cm 2.00 -4.00 -2.31 cm matrix of am cm = ym solve for cm 0.00 4.00 -2.31 cm matrix of am cm = ym solve for cm -1.00 0.00 4.62 tri_int1 running with np=30, nv=496 integral=0.071055, at i=8, j=8 intg fg =0.129654, at i=8 integral=-0.147640, at i=7, j=8 integral=0.085605, at i=3, j=8 finished k=3 computing local stiffness matrix for triangle 4 nodes i1=8, i2=7, i3=6, area=0.027061 coord (0.374989,0.216497) (0.125003,0.216505) (0.250000,0.000000) cm matrix of am cm = ym solve for cm -1.00 4.00 2.31 cm matrix of am cm = ym solve for cm 1.00 -4.00 2.31 cm matrix of am cm = ym solve for cm 1.00 -0.00 -4.62 tri_int1 running with np=30, nv=496 integral=0.154395, at i=8, j=8 intg fg =0.126709, at i=8 integral=-0.064313, at i=7, j=8 integral=-0.081061, at i=6, j=8 finished k=4 computing local stiffness matrix for triangle 5 nodes i1=7, i2=0, i3=6, area=0.027063 coord (0.125003,0.216505) (0.000000,0.000000) (0.250000,0.000000) cm matrix of am cm = ym solve for cm -0.00 -0.00 4.62 cm matrix of am cm = ym solve for cm 1.00 -4.00 -2.31 cm matrix of am cm = ym solve for cm 0.00 4.00 -2.31 tri_int1 running with np=30, nv=496 finished k=5 computing local stiffness matrix for triangle 6 nodes i1=6, i2=4, i3=8, area=0.027062 coord (0.250000,0.000000) (0.500000,0.000000) (0.374989,0.216497) cm matrix of am cm = ym solve for cm 2.00 -4.00 -2.31 cm matrix of am cm = ym solve for cm -1.00 4.00 -2.31 cm matrix of am cm = ym solve for cm -0.00 0.00 4.62 tri_int1 running with np=30, nv=496 integral=0.087810, at i=8, j=8 intg fg =0.126942, at i=8 integral=-0.147647, at i=6, j=8 integral=0.068857, at i=4, j=8 finished k=6 computing local stiffness matrix for triangle 7 nodes i1=9, i2=8, i3=4, area=0.027063 coord (0.624986,0.216511) (0.374989,0.216497) (0.500000,0.000000) cm matrix of am cm = ym solve for cm -2.00 4.00 2.31 cm matrix of am cm = ym solve for cm 2.00 -4.00 2.31 cm matrix of am cm = ym solve for cm 1.00 0.00 -4.62 tri_int1 running with np=30, nv=496 integral=0.154395, at i=9, j=9 intg fg =0.131227, at i=9 integral=-0.064321, at i=8, j=9 integral=-0.081053, at i=4, j=9 integral=-0.062117, at i=8, j=8 intg fg =0.130125, at i=8 integral=0.152191, at i=9, j=8 integral=-0.081053, at i=4, j=8 finished k=7 computing local stiffness matrix for triangle 8 nodes i1=10, i2=11, i3=2, area=0.027063 coord (0.874997,0.216505) (0.750000,0.000000) (1.000000,0.000000) cm matrix of am cm = ym solve for cm -0.00 0.00 4.62 cm matrix of am cm = ym solve for cm 4.00 -4.00 -2.31 cm matrix of am cm = ym solve for cm -3.00 4.00 -2.31 tri_int1 running with np=30, nv=496 finished k=8 computing local stiffness matrix for triangle 9 nodes i1=5, i2=12, i3=14, area=0.027064 coord (0.749994,0.433010) (0.625003,0.649495) (0.499975,0.432989) cm matrix of am cm = ym solve for cm -1.00 4.00 -2.31 cm matrix of am cm = ym solve for cm -2.00 -0.00 4.62 cm matrix of am cm = ym solve for cm 4.00 -4.00 -2.31 tri_int1 running with np=30, nv=496 integral=-0.145430, at i=14, j=14 intg fg =0.141197, at i=14 integral=0.068850, at i=5, j=14 integral=0.085602, at i=12, j=14 finished k=9 computing local stiffness matrix for triangle 10 nodes i1=9, i2=11, i3=10, area=0.027065 coord (0.624986,0.216511) (0.750000,0.000000) (0.874997,0.216505) cm matrix of am cm = ym solve for cm 3.00 -4.00 2.31 cm matrix of am cm = ym solve for cm 1.00 -0.00 -4.62 cm matrix of am cm = ym solve for cm -3.00 4.00 2.31 tri_int1 running with np=30, nv=496 integral=-0.062110, at i=9, j=9 intg fg =0.134645, at i=9 integral=-0.081068, at i=11, j=9 integral=0.152199, at i=10, j=9 finished k=10 computing local stiffness matrix for triangle 11 nodes i1=11, i2=9, i3=4, area=0.027064 coord (0.750000,0.000000) (0.624986,0.216511) (0.500000,0.000000) cm matrix of am cm = ym solve for cm -2.00 4.00 -2.31 cm matrix of am cm = ym solve for cm 0.00 -0.00 4.62 cm matrix of am cm = ym solve for cm 3.00 -4.00 -2.31 tri_int1 running with np=30, nv=496 integral=0.087810, at i=9, j=9 intg fg =0.131461, at i=9 integral=0.068866, at i=11, j=9 integral=-0.147655, at i=4, j=9 finished k=11 computing local stiffness matrix for triangle 12 nodes i1=12, i2=1, i3=13, area=0.027064 coord (0.625003,0.649495) (0.500000,0.866000) (0.374997,0.649495) cm matrix of am cm = ym solve for cm 0.00 4.00 -2.31 cm matrix of am cm = ym solve for cm -3.00 -0.00 4.62 cm matrix of am cm = ym solve for cm 4.00 -4.00 -2.31 tri_int1 running with np=30, nv=496 finished k=12 computing local stiffness matrix for triangle 13 nodes i1=13, i2=14, i3=12, area=0.027064 coord (0.374997,0.649495) (0.499975,0.432989) (0.625003,0.649495) cm matrix of am cm = ym solve for cm 1.00 -4.00 2.31 cm matrix of am cm = ym solve for cm 3.00 0.00 -4.62 cm matrix of am cm = ym solve for cm -3.00 4.00 2.31 tri_int1 running with np=30, nv=496 integral=-0.078858, at i=14, j=14 intg fg =0.140968, at i=14 integral=-0.064305, at i=13, j=14 integral=0.152185, at i=12, j=14 finished k=13 computing local stiffness matrix for triangle 14 nodes i1=14, i2=9, i3=5, area=0.027063 coord (0.499975,0.432989) (0.624986,0.216511) (0.749994,0.433010) cm matrix of am cm = ym solve for cm 2.00 -4.00 2.31 cm matrix of am cm = ym solve for cm 2.00 0.00 -4.62 cm matrix of am cm = ym solve for cm -3.00 4.00 2.31 tri_int1 running with np=30, nv=496 integral=-0.062103, at i=14, j=14 intg fg =0.138241, at i=14 integral=-0.081057, at i=9, j=14 integral=0.152181, at i=5, j=14 integral=-0.078853, at i=9, j=9 intg fg =0.137360, at i=9 integral=-0.064308, at i=14, j=9 integral=0.152181, at i=5, j=9 finished k=14 computing local stiffness matrix for triangle 15 nodes i1=13, i2=3, i3=14, area=0.027061 coord (0.374997,0.649495) (0.249994,0.432990) (0.499975,0.432989) cm matrix of am cm = ym solve for cm -2.00 0.00 4.62 cm matrix of am cm = ym solve for cm 3.00 -4.00 -2.31 cm matrix of am cm = ym solve for cm 0.00 4.00 -2.31 tri_int1 running with np=30, nv=496 integral=0.071061, at i=14, j=14 intg fg =0.137774, at i=14 integral=0.085600, at i=13, j=14 integral=-0.147641, at i=3, j=14 finished k=15 tri 0 has vertices 8 14 3 tri 1 has vertices 10 5 9 tri 2 has vertices 14 8 9 tri 3 has vertices 7 8 3 tri 4 has vertices 8 7 6 tri 5 has vertices 7 0 6 tri 6 has vertices 6 4 8 tri 7 has vertices 9 8 4 tri 8 has vertices 10 11 2 tri 9 has vertices 5 12 14 tri 10 has vertices 9 11 10 tri 11 has vertices 11 9 4 tri 12 has vertices 12 1 13 tri 13 has vertices 13 14 12 tri 14 has vertices 14 9 5 tri 15 has vertices 13 3 14 vertices, coordinates and analytic values coordinate 0 at 0.00 , 0.00, uana=1.000000 coordinate 1 at 0.50 , 0.87, uana=4.598000 coordinate 2 at 1.00 , 0.00, uana=3.000000 coordinate 3 at 0.25 , 0.43, uana=2.798960 coordinate 4 at 0.50 , 0.00, uana=2.000000 coordinate 5 at 0.75 , 0.43, uana=3.799018 coordinate 6 at 0.25 , 0.00, uana=1.500000 coordinate 7 at 0.13 , 0.22, uana=1.899520 coordinate 8 at 0.37 , 0.22, uana=2.399468 coordinate 9 at 0.62 , 0.22, uana=2.899506 coordinate 10 at 0.87 , 0.22, uana=3.399509 coordinate 11 at 0.75 , 0.00, uana=2.500000 coordinate 12 at 0.63 , 0.65, uana=4.198491 coordinate 13 at 0.37 , 0.65, uana=3.698480 coordinate 14 at 0.50 , 0.43, uana=3.298917 k computed stiffness matrix, if debug K(0,0)=1.000000 K(0,1)=0.000000 K(0,2)=0.000000 K(0,3)=0.000000 K(0,4)=0.000000 K(0,5)=0.000000 K(0,6)=0.000000 K(0,7)=0.000000 K(0,8)=0.000000 K(0,9)=0.000000 K(0,10)=0.000000 K(0,11)=0.000000 K(0,12)=0.000000 K(0,13)=0.000000 K(0,14)=0.000000 K(1,0)=0.000000 K(1,1)=1.000000 K(1,2)=0.000000 K(1,3)=0.000000 K(1,4)=0.000000 K(1,5)=0.000000 K(1,6)=0.000000 K(1,7)=0.000000 K(1,8)=0.000000 K(1,9)=0.000000 K(1,10)=0.000000 K(1,11)=0.000000 K(1,12)=0.000000 K(1,13)=0.000000 K(1,14)=0.000000 K(2,0)=0.000000 K(2,1)=0.000000 K(2,2)=1.000000 K(2,3)=0.000000 K(2,4)=0.000000 K(2,5)=0.000000 K(2,6)=0.000000 K(2,7)=0.000000 K(2,8)=0.000000 K(2,9)=0.000000 K(2,10)=0.000000 K(2,11)=0.000000 K(2,12)=0.000000 K(2,13)=0.000000 K(2,14)=0.000000 K(3,0)=0.000000 K(3,1)=0.000000 K(3,2)=0.000000 K(3,3)=1.000000 K(3,4)=0.000000 K(3,5)=0.000000 K(3,6)=0.000000 K(3,7)=0.000000 K(3,8)=0.000000 K(3,9)=0.000000 K(3,10)=0.000000 K(3,11)=0.000000 K(3,12)=0.000000 K(3,13)=0.000000 K(3,14)=0.000000 K(4,0)=0.000000 K(4,1)=0.000000 K(4,2)=0.000000 K(4,3)=0.000000 K(4,4)=1.000000 K(4,5)=0.000000 K(4,6)=0.000000 K(4,7)=0.000000 K(4,8)=0.000000 K(4,9)=0.000000 K(4,10)=0.000000 K(4,11)=0.000000 K(4,12)=0.000000 K(4,13)=0.000000 K(4,14)=0.000000 K(5,0)=0.000000 K(5,1)=0.000000 K(5,2)=0.000000 K(5,3)=0.000000 K(5,4)=0.000000 K(5,5)=1.000000 K(5,6)=0.000000 K(5,7)=0.000000 K(5,8)=0.000000 K(5,9)=0.000000 K(5,10)=0.000000 K(5,11)=0.000000 K(5,12)=0.000000 K(5,13)=0.000000 K(5,14)=0.000000 K(6,0)=0.000000 K(6,1)=0.000000 K(6,2)=0.000000 K(6,3)=0.000000 K(6,4)=0.000000 K(6,5)=0.000000 K(6,6)=1.000000 K(6,7)=0.000000 K(6,8)=0.000000 K(6,9)=0.000000 K(6,10)=0.000000 K(6,11)=0.000000 K(6,12)=0.000000 K(6,13)=0.000000 K(6,14)=0.000000 K(7,0)=0.000000 K(7,1)=0.000000 K(7,2)=0.000000 K(7,3)=0.000000 K(7,4)=0.000000 K(7,5)=0.000000 K(7,6)=0.000000 K(7,7)=1.000000 K(7,8)=0.000000 K(7,9)=0.000000 K(7,10)=0.000000 K(7,11)=0.000000 K(7,12)=0.000000 K(7,13)=0.000000 K(7,14)=0.000000 K(8,0)=0.000000 K(8,1)=0.000000 K(8,2)=0.000000 K(8,3)=0.021292 K(8,4)=-0.012196 K(8,5)=0.000000 K(8,6)=-0.228707 K(8,7)=-0.211953 K(8,8)=0.026858 K(8,9)=0.221047 K(8,10)=0.000000 K(8,11)=0.000000 K(8,12)=0.000000 K(8,13)=0.000000 K(8,14)=0.237781 K(9,0)=0.000000 K(9,1)=0.000000 K(9,2)=0.000000 K(9,3)=0.000000 K(9,4)=-0.228708 K(9,5)=0.237794 K(9,6)=0.000000 K(9,7)=0.000000 K(9,8)=-0.211959 K(9,9)=0.026860 K(9,10)=0.221051 K(9,11)=-0.012202 K(9,12)=0.000000 K(9,13)=0.000000 K(9,14)=0.021290 K(10,0)=0.000000 K(10,1)=0.000000 K(10,2)=0.000000 K(10,3)=0.000000 K(10,4)=0.000000 K(10,5)=0.000000 K(10,6)=0.000000 K(10,7)=0.000000 K(10,8)=0.000000 K(10,9)=0.000000 K(10,10)=1.000000 K(10,11)=0.000000 K(10,12)=0.000000 K(10,13)=0.000000 K(10,14)=0.000000 K(11,0)=0.000000 K(11,1)=0.000000 K(11,2)=0.000000 K(11,3)=0.000000 K(11,4)=0.000000 K(11,5)=0.000000 K(11,6)=0.000000 K(11,7)=0.000000 K(11,8)=0.000000 K(11,9)=0.000000 K(11,10)=0.000000 K(11,11)=1.000000 K(11,12)=0.000000 K(11,13)=0.000000 K(11,14)=0.000000 K(12,0)=0.000000 K(12,1)=0.000000 K(12,2)=0.000000 K(12,3)=0.000000 K(12,4)=0.000000 K(12,5)=0.000000 K(12,6)=0.000000 K(12,7)=0.000000 K(12,8)=0.000000 K(12,9)=0.000000 K(12,10)=0.000000 K(12,11)=0.000000 K(12,12)=1.000000 K(12,13)=0.000000 K(12,14)=0.000000 K(13,0)=0.000000 K(13,1)=0.000000 K(13,2)=0.000000 K(13,3)=0.000000 K(13,4)=0.000000 K(13,5)=0.000000 K(13,6)=0.000000 K(13,7)=0.000000 K(13,8)=0.000000 K(13,9)=0.000000 K(13,10)=0.000000 K(13,11)=0.000000 K(13,12)=0.000000 K(13,13)=1.000000 K(13,14)=0.000000 K(14,0)=0.000000 K(14,1)=0.000000 K(14,2)=0.000000 K(14,3)=-0.211953 K(14,4)=0.000000 K(14,5)=0.221031 K(14,6)=0.000000 K(14,7)=0.000000 K(14,8)=-0.228693 K(14,9)=-0.012201 K(14,10)=0.000000 K(14,11)=0.000000 K(14,12)=0.237786 K(14,13)=0.021295 K(14,14)=0.026859 f computed forcing function and boundary, if debug F(0)=1.000000, ug[0]=0.000000 F(1)=4.598000, ug[1]=0.000000 F(2)=3.000000, ug[2]=0.000000 F(3)=2.798960, ug[3]=0.000000 F(4)=2.000000, ug[4]=0.000000 F(5)=3.799018, ug[5]=0.000000 F(6)=1.500000, ug[6]=0.000000 F(7)=1.899520, ug[7]=0.000000 F(8)=0.779326, ug[8]=0.000000 F(9)=0.806453, ug[9]=0.000000 F(10)=3.399509, ug[10]=0.000000 F(11)=2.500000, ug[11]=0.000000 F(12)=4.198491, ug[12]=0.000000 F(13)=3.698480, ug[13]=0.000000 F(14)=0.828042, ug[14]=0.000000 ug computed Galerkin, Ua analytic, error ug[0]= 1.000, Ua= 1.000, err=0 ug[1]= 4.598, Ua= 4.598, err=0 ug[2]= 3.000, Ua= 3.000, err=0 ug[3]= 2.799, Ua= 2.799, err=0 ug[4]= 2.000, Ua= 2.000, err=0 ug[5]= 3.799, Ua= 3.799, err=0 ug[6]= 1.500, Ua= 1.500, err=0 ug[7]= 1.900, Ua= 1.900, err=0 ug[8]= 2.399, Ua= 2.399, err=-3.55271e-15 ug[9]= 2.900, Ua= 2.900, err=-2.4869e-14 ug[10]= 3.400, Ua= 3.400, err=0 ug[11]= 2.500, Ua= 2.500, err=0 ug[12]= 4.198, Ua= 4.198, err=0 ug[13]= 3.698, Ua= 3.698, err=0 ug[14]= 3.299, Ua= 3.299, err=1.90958e-14 maxerr=2.4869e-14, avgerr=3.16784e-15