A15_fem_50.out coordinates = 0 0 1.0000 1.5000 2.0000 3.0000 3.0000 4.5000 4.0000 6.0000 5.0000 4.5000 6.0000 3.0000 7.0000 1.5000 8.0000 0 6.0000 0 4.0000 0 2.0000 0 3.0000 1.5000 4.0000 3.0000 5.0000 1.5000 elements3 = 1 2 12 2 13 12 12 13 11 13 15 11 11 15 10 15 8 10 10 8 9 2 3 13 3 14 13 13 14 15 14 7 15 15 7 8 3 4 14 4 6 14 14 6 7 4 5 6 elements4 = [] dirichlet = 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 1 neumann = [] assembly from triangles A= (1,1) -0.5417 (2,1) 0.3333 (12,1) 0.2083 (1,2) 0.3333 (2,2) -1.7500 (3,2) 0.3333 (12,2) 0.6667 (13,2) 0.4167 (2,3) 0.3333 (3,3) -1.7500 (4,3) 0.3333 (13,3) 0.6667 (14,3) 0.4167 (3,4) 0.3333 (4,4) -1.7500 (5,4) 0.3333 (6,4) 0.4167 (14,4) 0.6667 (4,5) 0.3333 (5,5) -0.6667 (6,5) 0.3333 (4,6) 0.4167 (5,6) 0.3333 (6,6) -1.7500 (7,6) 0.3333 (14,6) 0.6667 (6,7) 0.3333 (7,7) -1.7500 (8,7) 0.3333 (14,7) 0.4167 (15,7) 0.6667 (7,8) 0.3333 (8,8) -1.7500 (9,8) 0.3333 (10,8) 0.6667 (15,8) 0.4167 (8,9) 0.3333 (9,9) -0.5417 (10,9) 0.2083 (8,10) 0.6667 (9,10) 0.2083 (10,10) -1.7500 (11,10) 0.2083 (15,10) 0.6667 (10,11) 0.2083 (11,11) -1.7500 (12,11) 0.2083 (13,11) 0.6667 (15,11) 0.6667 (1,12) 0.2083 (2,12) 0.6667 (11,12) 0.2083 (12,12) -1.7500 (13,12) 0.6667 (2,13) 0.4167 (3,13) 0.6667 (11,13) 0.6667 (12,13) 0.6667 (13,13) -3.5000 (14,13) 0.6667 (15,13) 0.4167 (3,14) 0.4167 (4,14) 0.6667 (6,14) 0.6667 (7,14) 0.4167 (13,14) 0.6667 (14,14) -3.5000 (15,14) 0.6667 (7,15) 0.6667 (8,15) 0.4167 (10,15) 0.6667 (11,15) 0.6667 (13,15) 0.4167 (14,15) 0.6667 (15,15) -3.5000 assembly from triangles and rectangles A= (1,1) -0.5417 (2,1) 0.3333 (12,1) 0.2083 (1,2) 0.3333 (2,2) -1.7500 (3,2) 0.3333 (12,2) 0.6667 (13,2) 0.4167 (2,3) 0.3333 (3,3) -1.7500 (4,3) 0.3333 (13,3) 0.6667 (14,3) 0.4167 (3,4) 0.3333 (4,4) -1.7500 (5,4) 0.3333 (6,4) 0.4167 (14,4) 0.6667 (4,5) 0.3333 (5,5) -0.6667 (6,5) 0.3333 (4,6) 0.4167 (5,6) 0.3333 (6,6) -1.7500 (7,6) 0.3333 (14,6) 0.6667 (6,7) 0.3333 (7,7) -1.7500 (8,7) 0.3333 (14,7) 0.4167 (15,7) 0.6667 (7,8) 0.3333 (8,8) -1.7500 (9,8) 0.3333 (10,8) 0.6667 (15,8) 0.4167 (8,9) 0.3333 (9,9) -0.5417 (10,9) 0.2083 (8,10) 0.6667 (9,10) 0.2083 (10,10) -1.7500 (11,10) 0.2083 (15,10) 0.6667 (10,11) 0.2083 (11,11) -1.7500 (12,11) 0.2083 (13,11) 0.6667 (15,11) 0.6667 (1,12) 0.2083 (2,12) 0.6667 (11,12) 0.2083 (12,12) -1.7500 (13,12) 0.6667 (2,13) 0.4167 (3,13) 0.6667 (11,13) 0.6667 (12,13) 0.6667 (13,13) -3.5000 (14,13) 0.6667 (15,13) 0.4167 (3,14) 0.4167 (4,14) 0.6667 (6,14) 0.6667 (7,14) 0.4167 (13,14) 0.6667 (14,14) -3.5000 (15,14) 0.6667 (7,15) 0.6667 (8,15) 0.4167 (10,15) 0.6667 (11,15) 0.6667 (13,15) 0.4167 (14,15) 0.6667 (15,15) -3.5000 forces from triangles b= (1,1) 0.4545 (2,1) 1.3636 (3,1) 1.3636 (4,1) 1.3636 (5,1) 0.4545 (6,1) 1.3636 (7,1) 1.3636 (8,1) 1.3636 (9,1) 0.4545 (10,1) 1.3636 (11,1) 1.3636 (12,1) 1.3636 (13,1) 2.7273 (14,1) 2.7273 (15,1) 2.7273 forces from triangles and rectangles b= (1,1) 0.4545 (2,1) 1.3636 (3,1) 1.3636 (4,1) 1.3636 (5,1) 0.4545 (6,1) 1.3636 (7,1) 1.3636 (8,1) 1.3636 (9,1) 0.4545 (10,1) 1.3636 (11,1) 1.3636 (12,1) 1.3636 (13,1) 2.7273 (14,1) 2.7273 (15,1) 2.7273 using g() add neumann conditions b= (1,1) 0.4545 (2,1) 1.3636 (3,1) 1.3636 (4,1) 1.3636 (5,1) 0.4545 (6,1) 1.3636 (7,1) 1.3636 (8,1) 1.3636 (9,1) 0.4545 (10,1) 1.3636 (11,1) 1.3636 (12,1) 1.3636 (13,1) 2.7273 (14,1) 2.7273 (15,1) 2.7273 BoundNodes= 1 2 3 4 5 6 7 8 9 10 11 12 using u_d() add dirichlet conditions u= (1,1) 1.0000 (2,1) 1.7955 (3,1) 4.1818 (4,1) 8.1591 (5,1) 13.7273 (6,1) 11.0682 (7,1) 10.0000 (8,1) 10.5227 (9,1) 12.6364 (10,1) 7.5455 (11,1) 3.9091 (12,1) 1.7273 apply u to b, dirichlet conditions b= (1,1) 0.0379 (2,1) 1.6269 (3,1) 5.3636 (4,1) 5.0606 (5,1) 3.1970 (6,1) 9.4242 (7,1) 11.6667 (8,1) 7.2027 (9,1) 2.2197 (10,1) 4.1061 (11,1) 6.2727 (12,1) 2.1667 (13,1) -4.5663 (14,1) -16.0000 (15,1) -15.9602 solve for A * u = b u= (1,1) 1.0000 (2,1) 1.7955 (3,1) 4.1818 (4,1) 8.1591 (5,1) 13.7273 (6,1) 11.0682 (7,1) 10.0000 (8,1) 10.5227 (9,1) 12.6364 (10,1) 7.5455 (11,1) 3.9091 (12,1) 1.7273 (13,1) 3.2500 (14,1) 6.3636 (15,1) 6.1591 1 x= 0 y= 0 solution= 1 2 x= 1 y= 1.5 solution= 1.7955 3 x= 2 y= 3 solution= 4.1818 4 x= 3 y= 4.5 solution= 8.1591 5 x= 4 y= 6 solution= 13.7273 6 x= 5 y= 4.5 solution= 11.0682 7 x= 6 y= 3 solution= 10 8 x= 7 y= 1.5 solution= 10.5227 9 x= 8 y= 0 solution= 12.6364 10 x= 6 y= 0 solution= 7.5455 11 x= 4 y= 0 solution= 3.9091 12 x= 2 y= 0 solution= 1.7273 13 x= 3 y= 1.5 solution= 3.25 14 x= 4 y= 3 solution= 6.3636 15 x= 5 y= 1.5 solution= 6.1591