27 December 2010 8:47:43.066 AM FREE_FEM_STOKES FORTRAN90 version: Finite element solution of the steady incompressible Stokes equations on a triangulated region in 2 dimensions. -nu * ( Uxx + Uyy ) + dPdx = F1(x,y) -nu * ( Vxx + Vyy ) + dPdy = F2(x,y) Ux + Vy = F3(x,y). Boundary conditions may be of Dirichlet type: U(x,y) = U_BC(x,y) V(x,y) = V_BC(x,y) P(x,y) = P_BC(x,y) or of Neumann type with zero right hand side: dU/dn(x,y) = 0 dV/dn(x,y) = 0 dP/dn(x,y) = 0 The finite element method uses Taylor-Hood triangular elements which are linear for pressure and quadratic for velocity. Quadrature order = 7 The kinematic viscosity NU = 1.00000 Current status: * testing zero Neumann condition option. Node file is "nodes6.txt". Element file is "triangles6.txt". Number of nodes = 65 First 10 nodes Row 1 2 Col 1 0.00000 0.00000 2 0.00000 0.250000 3 0.00000 0.500000 4 0.00000 0.750000 5 0.00000 1.00000 6 0.250000 0.00000 7 0.250000 0.250000 8 0.250000 0.500000 9 0.250000 0.750000 10 0.250000 1.00000 Element order = 6 Number of elements = 24 First 10 elements Row 1 2 3 4 5 6 Col 1 1 11 3 6 7 2 2 13 3 11 8 7 12 3 3 13 5 8 9 4 4 15 5 13 10 9 14 5 11 21 13 16 17 12 6 23 13 21 18 17 22 7 13 23 15 18 19 14 8 25 15 23 20 19 24 9 21 31 23 26 27 22 10 33 23 31 28 27 32 Dirichlet boundary condition on pressure will be applied at node 1 Number of Neumann conditions added = 6 Boundary conditions per node: Node U_cond V_cond P_cond 1 2 2 2 2 2 2 0 3 2 2 1 4 2 2 0 5 2 2 1 6 2 2 0 7 1 1 0 8 1 1 0 9 1 1 0 10 2 2 0 11 2 2 1 12 1 1 0 13 1 1 1 14 1 1 0 15 2 2 1 16 2 2 0 17 1 1 0 18 1 1 0 19 1 1 0 20 2 2 0 21 2 2 1 22 1 1 0 23 1 1 1 24 1 1 0 25 2 2 1 26 2 2 0 27 1 1 0 28 1 1 0 29 1 1 0 30 2 2 0 31 2 2 1 32 1 1 0 33 1 1 1 34 1 1 0 35 2 2 1 36 2 2 0 37 1 1 0 38 1 1 0 39 1 1 0 40 2 2 0 41 2 2 1 42 1 1 0 43 1 1 1 44 1 1 0 45 2 2 1 46 2 2 0 47 1 1 0 48 1 1 0 49 1 1 0 50 2 2 0 51 2 2 1 52 1 1 0 53 1 1 1 54 1 1 0 55 2 2 1 56 2 2 0 57 1 1 0 58 1 1 0 59 1 1 0 60 2 2 0 61 2 2 1 62 3 3 0 63 3 3 1 64 3 3 0 65 2 2 1 Total number of variables is 151 Variable indices per node: Node U_index V_index P_index 1 1 2 3 2 4 5 -1 3 6 7 8 4 9 10 -1 5 11 12 13 6 14 15 -1 7 16 17 -1 8 18 19 -1 9 20 21 -1 10 22 23 -1 11 24 25 26 12 27 28 -1 13 29 30 31 14 32 33 -1 15 34 35 36 16 37 38 -1 17 39 40 -1 18 41 42 -1 19 43 44 -1 20 45 46 -1 21 47 48 49 22 50 51 -1 23 52 53 54 24 55 56 -1 25 57 58 59 26 60 61 -1 27 62 63 -1 28 64 65 -1 29 66 67 -1 30 68 69 -1 31 70 71 72 32 73 74 -1 33 75 76 77 34 78 79 -1 35 80 81 82 36 83 84 -1 37 85 86 -1 38 87 88 -1 39 89 90 -1 40 91 92 -1 41 93 94 95 42 96 97 -1 43 98 99 100 44 101 102 -1 45 103 104 105 46 106 107 -1 47 108 109 -1 48 110 111 -1 49 112 113 -1 50 114 115 -1 51 116 117 118 52 119 120 -1 53 121 122 123 54 124 125 -1 55 126 127 128 56 129 130 -1 57 131 132 -1 58 133 134 -1 59 135 136 -1 60 137 138 -1 61 139 140 141 62 142 143 -1 63 144 145 146 64 147 148 -1 65 149 150 151 The matrix half bandwidth is 25 The matrix bandwidth is 51 The storage bandwidth is 76 Order 6 nodes plotted in "nodes6.eps". Order 6 triangles plotted in "triangles6.eps". Part of Stokes matrix, adjusted for Dirichlet BC: Col: 1 2 3 4 5 Row --- 1 1.00000 0.00000 0.00000 0.00000 0.00000 2 0.00000 1.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 1.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 1.00000 0.00000 5 0.00000 0.00000 0.00000 0.00000 1.00000 6 0.00000 0.00000 0.00000 0.00000 0.00000 7 0.00000 0.00000 0.00000 0.00000 0.00000 8 -0.277556E-16 -0.277556E-16 0.00000 -0.166667 -0.833333E-01 9 0.00000 0.00000 0.00000 0.00000 0.00000 10 0.00000 0.00000 0.00000 0.00000 0.00000 11 0.00000 0.00000 0.00000 0.00000 0.00000 12 0.00000 0.00000 0.00000 0.00000 0.00000 13 0.00000 0.00000 0.00000 0.00000 0.00000 14 0.00000 0.00000 0.00000 0.00000 0.00000 15 0.00000 0.00000 0.00000 0.00000 0.00000 16 -0.444089E-15 0.00000 -0.833333E-01 -1.33333 0.00000 17 0.00000 -0.444089E-15 -0.833333E-01 0.00000 -1.33333 18 0.00000 0.00000 0.00000 0.00000 0.00000 19 0.00000 0.00000 0.00000 0.00000 0.00000 20 0.00000 0.00000 0.00000 0.00000 0.00000 Col: 6 7 8 9 10 Row --- 1 0.00000 0.00000 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 0.00000 0.00000 5 0.00000 0.00000 0.00000 0.00000 0.00000 6 1.00000 0.00000 0.00000 0.00000 0.00000 7 0.00000 1.00000 0.00000 0.00000 0.00000 8 -0.166667 -0.416334E-16 0.00000 -0.833333E-01 0.833333E-01 9 0.00000 0.00000 0.00000 1.00000 0.00000 10 0.00000 0.00000 0.00000 0.00000 1.00000 11 0.00000 0.00000 0.00000 0.00000 0.00000 12 0.00000 0.00000 0.00000 0.00000 0.00000 13 -0.173472E-16 -0.173472E-16 0.00000 -0.166667 -0.833333E-01 14 0.00000 0.00000 0.00000 0.00000 0.00000 15 0.00000 0.00000 0.00000 0.00000 0.00000 16 -0.152656E-15 0.00000 -0.833333E-01 0.00000 0.00000 17 0.00000 -0.152656E-15 0.833333E-01 0.00000 0.00000 18 -1.33333 0.00000 -0.166667 -0.388578E-15 0.00000 19 0.00000 -1.33333 -0.833333E-01 0.00000 -0.388578E-15 20 -0.333067E-15 0.00000 -0.833333E-01 -1.33333 0.00000 Col: 11 12 13 14 15 Row --- 1 0.00000 0.00000 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 0.00000 0.00000 5 0.00000 0.00000 0.00000 0.00000 0.00000 6 0.00000 0.00000 0.00000 0.00000 0.00000 7 0.00000 0.00000 0.00000 0.00000 0.00000 8 0.00000 -0.650521E-18 0.00000 0.381639E-16 -0.833333E-01 9 0.00000 0.00000 0.00000 0.00000 0.00000 10 0.00000 0.00000 0.00000 0.00000 0.00000 11 1.00000 0.00000 0.00000 0.00000 0.00000 12 0.00000 1.00000 0.00000 0.00000 0.00000 13 -0.833333E-01 0.833333E-01 0.00000 0.00000 0.00000 14 0.00000 0.00000 0.00000 1.00000 0.00000 15 0.00000 0.00000 0.00000 0.00000 1.00000 16 0.00000 0.00000 0.00000 -1.33333 0.00000 17 0.00000 0.00000 0.00000 0.00000 -1.33333 18 0.277556E-16 0.00000 0.00000 0.00000 0.00000 19 0.00000 0.277556E-16 0.833333E-01 0.00000 0.00000 20 -0.124900E-15 0.00000 -0.833333E-01 0.00000 0.00000 Col: 16 17 18 19 20 Row --- 1 0.00000 0.00000 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 0.00000 0.00000 5 0.00000 0.00000 0.00000 0.00000 0.00000 6 0.00000 0.00000 0.00000 0.00000 0.00000 7 0.00000 0.00000 0.00000 0.00000 0.00000 8 0.833333E-01 -0.833333E-01 0.166667 0.833333E-01 0.833333E-01 9 0.00000 0.00000 0.00000 0.00000 0.00000 10 0.00000 0.00000 0.00000 0.00000 0.00000 11 0.00000 0.00000 0.00000 0.00000 0.00000 12 0.00000 0.00000 0.00000 0.00000 0.00000 13 0.00000 0.00000 0.312250E-16 -0.833333E-01 0.833333E-01 14 0.00000 0.00000 0.00000 0.00000 0.00000 15 0.00000 0.00000 0.00000 0.00000 0.00000 16 5.33333 0.00000 -1.33333 0.00000 0.00000 17 0.00000 5.33333 0.00000 -1.33333 0.00000 18 -1.33333 0.00000 5.33333 0.00000 -1.33333 19 0.00000 -1.33333 0.00000 5.33333 0.00000 20 0.00000 0.00000 -1.33333 0.00000 5.33333 Part of Stokes right hand side, adjusted for Dirichlet BC: 1 0.0000000 2 0.0000000 3 0.0000000 4 0.18750000 5 0.0000000 6 0.25000000 7 0.0000000 8 0.0000000 9 0.18750000 10 0.0000000 11 0.0000000 12 0.0000000 13 0.0000000 14 0.0000000 15 0.0000000 16 0.0000000 17 0.0000000 18 0.0000000 19 0.0000000 20 0.0000000 Part of Stokes matrix, adjusted for Dirichlet BC: Col: Row --- Col: Row --- Col: Row --- Col: Row --- Col: Row --- Part of Stokes right hand side, adjusted for Dirichlet BC: Part of Stokes matrix, adjusted for Neumann BC: Col: 1 2 3 4 5 Row --- 1 1.00000 0.00000 0.00000 0.00000 0.00000 2 0.00000 1.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 1.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 1.00000 0.00000 5 0.00000 0.00000 0.00000 0.00000 1.00000 6 0.00000 0.00000 0.00000 0.00000 0.00000 7 0.00000 0.00000 0.00000 0.00000 0.00000 8 -0.277556E-16 -0.277556E-16 0.00000 -0.166667 -0.833333E-01 9 0.00000 0.00000 0.00000 0.00000 0.00000 10 0.00000 0.00000 0.00000 0.00000 0.00000 11 0.00000 0.00000 0.00000 0.00000 0.00000 12 0.00000 0.00000 0.00000 0.00000 0.00000 13 0.00000 0.00000 0.00000 0.00000 0.00000 14 0.00000 0.00000 0.00000 0.00000 0.00000 15 0.00000 0.00000 0.00000 0.00000 0.00000 16 -0.444089E-15 0.00000 -0.833333E-01 -1.33333 0.00000 17 0.00000 -0.444089E-15 -0.833333E-01 0.00000 -1.33333 18 0.00000 0.00000 0.00000 0.00000 0.00000 19 0.00000 0.00000 0.00000 0.00000 0.00000 20 0.00000 0.00000 0.00000 0.00000 0.00000 Col: 6 7 8 9 10 Row --- 1 0.00000 0.00000 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 0.00000 0.00000 5 0.00000 0.00000 0.00000 0.00000 0.00000 6 1.00000 0.00000 0.00000 0.00000 0.00000 7 0.00000 1.00000 0.00000 0.00000 0.00000 8 -0.166667 -0.416334E-16 0.00000 -0.833333E-01 0.833333E-01 9 0.00000 0.00000 0.00000 1.00000 0.00000 10 0.00000 0.00000 0.00000 0.00000 1.00000 11 0.00000 0.00000 0.00000 0.00000 0.00000 12 0.00000 0.00000 0.00000 0.00000 0.00000 13 -0.173472E-16 -0.173472E-16 0.00000 -0.166667 -0.833333E-01 14 0.00000 0.00000 0.00000 0.00000 0.00000 15 0.00000 0.00000 0.00000 0.00000 0.00000 16 -0.152656E-15 0.00000 -0.833333E-01 0.00000 0.00000 17 0.00000 -0.152656E-15 0.833333E-01 0.00000 0.00000 18 -1.33333 0.00000 -0.166667 -0.388578E-15 0.00000 19 0.00000 -1.33333 -0.833333E-01 0.00000 -0.388578E-15 20 -0.333067E-15 0.00000 -0.833333E-01 -1.33333 0.00000 Col: 11 12 13 14 15 Row --- 1 0.00000 0.00000 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 0.00000 0.00000 5 0.00000 0.00000 0.00000 0.00000 0.00000 6 0.00000 0.00000 0.00000 0.00000 0.00000 7 0.00000 0.00000 0.00000 0.00000 0.00000 8 0.00000 -0.650521E-18 0.00000 0.381639E-16 -0.833333E-01 9 0.00000 0.00000 0.00000 0.00000 0.00000 10 0.00000 0.00000 0.00000 0.00000 0.00000 11 1.00000 0.00000 0.00000 0.00000 0.00000 12 0.00000 1.00000 0.00000 0.00000 0.00000 13 -0.833333E-01 0.833333E-01 0.00000 0.00000 0.00000 14 0.00000 0.00000 0.00000 1.00000 0.00000 15 0.00000 0.00000 0.00000 0.00000 1.00000 16 0.00000 0.00000 0.00000 -1.33333 0.00000 17 0.00000 0.00000 0.00000 0.00000 -1.33333 18 0.277556E-16 0.00000 0.00000 0.00000 0.00000 19 0.00000 0.277556E-16 0.833333E-01 0.00000 0.00000 20 -0.124900E-15 0.00000 -0.833333E-01 0.00000 0.00000 Col: 16 17 18 19 20 Row --- 1 0.00000 0.00000 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 0.00000 0.00000 5 0.00000 0.00000 0.00000 0.00000 0.00000 6 0.00000 0.00000 0.00000 0.00000 0.00000 7 0.00000 0.00000 0.00000 0.00000 0.00000 8 0.833333E-01 -0.833333E-01 0.166667 0.833333E-01 0.833333E-01 9 0.00000 0.00000 0.00000 0.00000 0.00000 10 0.00000 0.00000 0.00000 0.00000 0.00000 11 0.00000 0.00000 0.00000 0.00000 0.00000 12 0.00000 0.00000 0.00000 0.00000 0.00000 13 0.00000 0.00000 0.312250E-16 -0.833333E-01 0.833333E-01 14 0.00000 0.00000 0.00000 0.00000 0.00000 15 0.00000 0.00000 0.00000 0.00000 0.00000 16 5.33333 0.00000 -1.33333 0.00000 0.00000 17 0.00000 5.33333 0.00000 -1.33333 0.00000 18 -1.33333 0.00000 5.33333 0.00000 -1.33333 19 0.00000 -1.33333 0.00000 5.33333 0.00000 20 0.00000 0.00000 -1.33333 0.00000 5.33333 Part of Stokes right hand side, adjusted for Neumann BC: 1 0.0000000 2 0.0000000 3 0.0000000 4 0.18750000 5 0.0000000 6 0.25000000 7 0.0000000 8 0.0000000 9 0.18750000 10 0.0000000 11 0.0000000 12 0.0000000 13 0.0000000 14 0.0000000 15 0.0000000 16 0.0000000 17 0.0000000 18 0.0000000 19 0.0000000 20 0.0000000 Part of Stokes matrix, adjusted for Neumann BC: Col: Row --- Col: Row --- Col: Row --- Col: Row --- Col: Row --- Part of Stokes right hand side, adjusted for Neumann BC: Variables associated with nodes: Node U V P 1 0.00000 0.00000 0.00000 2 0.187500 0.108912E-15 3 0.250000 -0.533262E-16 -0.435780E-10 4 0.187500 0.208167E-15 5 0.00000 0.00000 -0.399737E-10 6 0.00000 0.00000 7 0.187500 0.593608E-12 8 0.250000 0.157504E-13 9 0.187500 -0.277494E-14 10 0.00000 0.00000 11 0.00000 0.624500E-16 -1.00000 12 0.187500 -0.319900E-13 13 0.250000 0.305626E-13 -1.00000 14 0.187500 0.780410E-13 15 0.00000 0.00000 -1.00000 16 0.333067E-15 0.00000 17 0.187500 -0.860121E-13 18 0.250000 0.280432E-13 19 0.187500 0.439499E-13 20 0.00000 0.00000 21 0.00000 0.00000 -2.00000 22 0.187500 -0.176159E-13 23 0.250000 -0.697675E-14 -2.00000 24 0.187500 -0.130314E-13 25 0.00000 0.00000 -2.00000 26 -0.00000 0.00000 27 0.187500 0.129965E-14 28 0.250000 -0.108017E-13 29 0.187500 -0.145650E-13 30 0.00000 0.00000 31 0.00000 0.00000 -3.00000 32 0.187500 0.870520E-14 33 0.250000 0.126876E-16 -3.00000 34 0.187500 -0.119192E-14 35 0.00000 0.00000 -3.00000 36 -0.166533E-15 0.00000 37 0.187500 0.475401E-14 38 0.250000 0.163831E-14 39 0.187500 0.156009E-14 40 0.00000 0.00000 41 0.00000 0.00000 -4.00000 42 0.187500 -0.118664E-14 43 0.250000 0.571118E-15 -4.00000 44 0.187500 0.971223E-15 45 0.00000 0.00000 -4.00000 46 0.333067E-15 0.00000 47 0.187500 -0.118535E-14 48 0.250000 0.173997E-15 49 0.187500 0.252876E-15 50 0.00000 0.00000 51 0.00000 0.00000 -5.00000 52 0.187500 0.393546E-16 53 0.250000 -0.761406E-16 -5.00000 54 0.187500 -0.207262E-15 55 0.00000 0.00000 -5.00000 56 -0.00000 0.00000 57 0.187500 0.293579E-15 58 0.250000 -0.00000 59 0.187500 -0.240856E-16 60 0.00000 0.00000 61 0.00000 0.00000 -6.00000 62 0.187500 0.281224E-15 63 0.250000 0.113480E-15 -6.00000 64 0.187500 0.237551E-15 65 0.00000 0.00000 -6.00000 Pressure nodes written to "nodes3.txt". Pressure triangles written to "triangles3.txt". Pressures written to "pressure3.txt". Velocities written to "velocity6.txt". FREE_FEM_STOKES: Normal end of execution. 27 December 2010 8:47:43.075 AM