>> fem2d_linear ( 17, 17 ) FEM2D_LINEAR MATLAB version Solution of the Poisson equation: - Uxx - Uyy = F(x,y) inside the region, U(x,y) = G(x,y) on the boundary of the region. The region is a rectangle, defined by: 0.000000 = XL<= X <= XR = 1.000000 0.000000 = YB<= Y <= YT = 1.000000 The finite element method is used, with piecewise linear basis functions on 3 node triangular elements. The corner nodes of the triangles are generated by an underlying grid whose dimensions are NX = 17 NY = 17 Number of nodes = 289 Number of elements = 512 K I J X Y U U exact computed 1 1 1 0.000000 0.000000 0.000000e+00 0.000000e+00 0.000000e+00 2 2 1 0.062500 0.000000 6.250000e-02 6.250000e-02 0.000000e+00 3 3 1 0.125000 0.000000 1.250000e-01 1.250000e-01 0.000000e+00 4 4 1 0.187500 0.000000 1.875000e-01 1.875000e-01 0.000000e+00 5 5 1 0.250000 0.000000 2.500000e-01 2.500000e-01 0.000000e+00 6 6 1 0.312500 0.000000 3.125000e-01 3.125000e-01 0.000000e+00 7 7 1 0.375000 0.000000 3.750000e-01 3.750000e-01 0.000000e+00 8 8 1 0.437500 0.000000 4.375000e-01 4.375000e-01 0.000000e+00 9 9 1 0.500000 0.000000 5.000000e-01 5.000000e-01 0.000000e+00 10 10 1 0.562500 0.000000 5.625000e-01 5.625000e-01 0.000000e+00 11 11 1 0.625000 0.000000 6.250000e-01 6.250000e-01 0.000000e+00 12 12 1 0.687500 0.000000 6.875000e-01 6.875000e-01 0.000000e+00 13 13 1 0.750000 0.000000 7.500000e-01 7.500000e-01 0.000000e+00 14 14 1 0.812500 0.000000 8.125000e-01 8.125000e-01 0.000000e+00 15 15 1 0.875000 0.000000 8.750000e-01 8.750000e-01 0.000000e+00 16 16 1 0.937500 0.000000 9.375000e-01 9.375000e-01 0.000000e+00 17 17 1 1.000000 0.000000 1.000000e+00 1.000000e+00 0.000000e+00 18 1 2 0.000000 0.062500 0.000000e+00 0.000000e+00 0.000000e+00 19 2 2 0.062500 0.062500 1.005602e-01 1.002247e-01 3.355313e-04 20 3 2 0.125000 0.062500 1.996578e-01 1.991102e-01 5.475957e-04 21 4 2 0.187500 0.062500 2.958864e-01 2.952056e-01 6.807946e-04 22 5 2 0.250000 0.062500 3.879497e-01 3.871949e-01 7.547793e-04 23 6 2 0.312500 0.062500 4.747117e-01 4.739317e-01 7.799600e-04 24 7 2 0.375000 0.062500 5.552400e-01 5.544767e-01 7.632324e-04 25 8 2 0.437500 0.062500 6.288417e-01 6.281314e-01 7.103587e-04 26 9 2 0.500000 0.062500 6.950903e-01 6.944632e-01 6.270814e-04 27 10 2 0.562500 0.062500 7.538417e-01 7.533220e-01 5.197056e-04 28 11 2 0.625000 0.062500 8.052400e-01 8.048445e-01 3.954629e-04 29 12 2 0.687500 0.062500 8.497117e-01 8.494488e-01 2.628382e-04 30 13 2 0.750000 0.062500 8.879497e-01 8.878176e-01 1.320477e-04 31 14 2 0.812500 0.062500 9.208864e-01 9.208704e-01 1.598088e-05 32 15 2 0.875000 0.062500 9.496578e-01 9.497255e-01 6.764839e-05 33 16 2 0.937500 0.062500 9.755602e-01 9.756511e-01 9.085629e-05 34 17 2 1.000000 0.062500 1.000000e+00 1.000000e+00 0.000000e+00 35 1 3 0.000000 0.125000 0.000000e+00 0.000000e+00 0.000000e+00 36 2 3 0.062500 0.125000 1.371578e-01 1.366102e-01 5.475957e-04 37 3 3 0.125000 0.125000 2.714466e-01 2.705147e-01 9.318634e-04 38 4 3 0.187500 0.125000 4.001075e-01 3.989149e-01 1.192658e-03 39 5 3 0.250000 0.125000 5.205981e-01 5.192450e-01 1.353032e-03 40 6 3 0.312500 0.125000 6.306896e-01 6.292624e-01 1.427204e-03 41 7 3 0.375000 0.125000 7.285534e-01 7.271280e-01 1.425403e-03 42 8 3 0.437500 0.125000 8.128303e-01 8.114737e-01 1.356603e-03 43 9 3 0.500000 0.125000 8.826834e-01 8.814534e-01 1.230064e-03 44 10 3 0.562500 0.125000 9.378303e-01 9.367740e-01 1.056256e-03 45 11 3 0.625000 0.125000 9.785534e-01 9.777059e-01 8.474596e-04 46 12 3 0.687500 0.125000 1.005690e+00 1.005071e+00 6.183187e-04 47 13 3 0.750000 0.125000 1.020598e+00 1.020212e+00 3.865419e-04 48 14 3 0.812500 0.125000 1.025108e+00 1.024933e+00 1.741166e-04 49 15 3 0.875000 0.125000 1.021447e+00 1.021437e+00 9.587131e-06 50 16 3 0.937500 0.125000 1.012158e+00 1.012225e+00 6.764839e-05 51 17 3 1.000000 0.125000 1.000000e+00 1.000000e+00 0.000000e+00 52 1 4 0.000000 0.187500 0.000000e+00 0.000000e+00 0.000000e+00 53 2 4 0.062500 0.187500 1.708864e-01 1.702056e-01 6.807946e-04 54 3 4 0.125000 0.187500 3.376075e-01 3.364149e-01 1.192658e-03 55 4 4 0.187500 0.187500 4.961583e-01 4.945956e-01 1.562731e-03 56 5 4 0.250000 0.187500 6.428475e-01 6.410382e-01 1.809321e-03 57 6 4 0.312500 0.187500 7.744398e-01 7.724947e-01 1.945068e-03 58 7 4 0.375000 0.187500 8.882800e-01 8.863000e-01 1.979926e-03 59 8 4 0.437500 0.187500 9.823951e-01 9.804718e-01 1.923353e-03 60 9 4 0.500000 0.187500 1.055570e+00 1.053784e+00 1.785777e-03 61 10 4 0.562500 0.187500 1.107395e+00 1.105816e+00 1.579574e-03 62 11 4 0.625000 0.187500 1.138280e+00 1.136960e+00 1.319759e-03 63 12 4 0.687500 0.187500 1.149440e+00 1.148415e+00 1.024571e-03 64 13 4 0.750000 0.187500 1.142847e+00 1.142131e+00 7.161482e-04 65 14 4 0.812500 0.187500 1.121158e+00 1.120737e+00 4.215177e-04 66 15 4 0.875000 0.187500 1.087608e+00 1.087433e+00 1.741166e-04 67 16 4 0.937500 0.187500 1.045886e+00 1.045870e+00 1.598088e-05 68 17 4 1.000000 0.187500 1.000000e+00 1.000000e+00 0.000000e+00 69 1 5 0.000000 0.250000 0.000000e+00 0.000000e+00 0.000000e+00 70 2 5 0.062500 0.250000 2.004497e-01 1.996949e-01 7.547793e-04 71 3 5 0.125000 0.250000 3.955981e-01 3.942450e-01 1.353032e-03 72 4 5 0.187500 0.250000 5.803475e-01 5.785382e-01 1.809321e-03 73 5 5 0.250000 0.250000 7.500000e-01 7.478658e-01 2.134224e-03 74 6 5 0.312500 0.250000 9.004378e-01 8.981022e-01 2.335632e-03 75 7 5 0.375000 0.250000 1.028281e+00 1.025861e+00 2.420504e-03 76 8 5 0.437500 0.250000 1.131020e+00 1.128623e+00 2.396436e-03 77 9 5 0.500000 0.250000 1.207107e+00 1.204834e+00 2.272863e-03 78 10 5 0.562500 0.250000 1.256020e+00 1.253958e+00 2.061945e-03 79 11 5 0.625000 0.250000 1.278281e+00 1.276502e+00 1.779198e-03 80 12 5 0.687500 0.250000 1.275438e+00 1.273994e+00 1.444001e-03 81 13 5 0.750000 0.250000 1.250000e+00 1.248920e+00 1.080089e-03 82 14 5 0.812500 0.250000 1.205347e+00 1.204631e+00 7.161482e-04 83 15 5 0.875000 0.250000 1.145598e+00 1.145212e+00 3.865419e-04 84 16 5 0.937500 0.250000 1.075450e+00 1.075318e+00 1.320477e-04 85 17 5 1.000000 0.250000 1.000000e+00 1.000000e+00 0.000000e+00 86 1 6 0.000000 0.312500 0.000000e+00 0.000000e+00 0.000000e+00 87 2 6 0.062500 0.312500 2.247117e-01 2.239317e-01 7.799600e-04 88 3 6 0.125000 0.312500 4.431896e-01 4.417624e-01 1.427204e-03 89 4 6 0.187500 0.312500 6.494398e-01 6.474947e-01 1.945068e-03 90 5 6 0.250000 0.312500 8.379378e-01 8.356022e-01 2.335632e-03 91 6 6 0.312500 0.312500 1.003842e+00 1.001241e+00 2.600476e-03 92 7 6 0.375000 0.312500 1.143178e+00 1.140436e+00 2.741814e-03 93 8 6 0.437500 0.312500 1.252993e+00 1.250230e+00 2.763626e-03 94 9 6 0.500000 0.312500 1.331470e+00 1.328797e+00 2.672604e-03 95 10 6 0.562500 0.312500 1.377993e+00 1.375514e+00 2.478875e-03 96 11 6 0.625000 0.312500 1.393178e+00 1.390981e+00 2.196514e-03 97 12 6 0.687500 0.312500 1.378842e+00 1.376998e+00 1.843902e-03 98 13 6 0.750000 0.312500 1.337938e+00 1.336494e+00 1.444001e-03 99 14 6 0.812500 0.312500 1.274440e+00 1.273415e+00 1.024571e-03 100 15 6 0.875000 0.312500 1.193190e+00 1.192571e+00 6.183187e-04 101 16 6 0.937500 0.312500 1.099712e+00 1.099449e+00 2.628382e-04 102 17 6 1.000000 0.312500 1.000000e+00 1.000000e+00 0.000000e+00 103 1 7 0.000000 0.375000 0.000000e+00 0.000000e+00 0.000000e+00 104 2 7 0.062500 0.375000 2.427400e-01 2.419767e-01 7.632324e-04 105 3 7 0.125000 0.375000 4.785534e-01 4.771280e-01 1.425403e-03 106 4 7 0.187500 0.375000 7.007800e-01 6.988000e-01 1.979926e-03 107 5 7 0.250000 0.375000 9.032815e-01 9.008610e-01 2.420504e-03 108 6 7 0.312500 0.375000 1.080678e+00 1.077936e+00 2.741814e-03 109 7 7 0.375000 0.375000 1.228553e+00 1.225613e+00 2.940374e-03 110 8 7 0.437500 0.375000 1.343627e+00 1.340612e+00 3.015419e-03 111 9 7 0.500000 0.375000 1.423880e+00 1.420910e+00 2.969638e-03 112 10 7 0.562500 0.375000 1.468627e+00 1.465818e+00 2.809735e-03 113 11 7 0.625000 0.375000 1.478553e+00 1.476007e+00 2.546801e-03 114 12 7 0.687500 0.375000 1.455678e+00 1.453481e+00 2.196514e-03 115 13 7 0.750000 0.375000 1.403281e+00 1.401502e+00 1.779198e-03 116 14 7 0.812500 0.375000 1.325780e+00 1.324460e+00 1.319759e-03 117 15 7 0.875000 0.375000 1.228553e+00 1.227706e+00 8.474596e-04 118 16 7 0.937500 0.375000 1.117740e+00 1.117344e+00 3.954629e-04 119 17 7 1.000000 0.375000 1.000000e+00 1.000000e+00 0.000000e+00 120 1 8 0.000000 0.437500 0.000000e+00 0.000000e+00 0.000000e+00 121 2 8 0.062500 0.437500 2.538417e-01 2.531314e-01 7.103587e-04 122 3 8 0.125000 0.437500 5.003303e-01 4.989737e-01 1.356603e-03 123 4 8 0.187500 0.437500 7.323951e-01 7.304718e-01 1.923353e-03 124 5 8 0.250000 0.437500 9.435199e-01 9.411235e-01 2.396436e-03 125 6 8 0.312500 0.437500 1.127993e+00 1.125230e+00 2.763626e-03 126 7 8 0.375000 0.437500 1.281127e+00 1.278112e+00 3.015419e-03 127 8 8 0.437500 0.437500 1.399440e+00 1.396294e+00 3.145746e-03 128 9 8 0.500000 0.437500 1.480785e+00 1.477633e+00 3.152551e-03 129 10 8 0.562500 0.437500 1.524440e+00 1.521402e+00 3.038205e-03 130 11 8 0.625000 0.437500 1.531127e+00 1.528318e+00 2.809735e-03 131 12 8 0.687500 0.437500 1.502993e+00 1.500514e+00 2.478875e-03 132 13 8 0.750000 0.437500 1.443520e+00 1.441458e+00 2.061945e-03 133 14 8 0.812500 0.437500 1.357395e+00 1.355816e+00 1.579574e-03 134 15 8 0.875000 0.437500 1.250330e+00 1.249274e+00 1.056256e-03 135 16 8 0.937500 0.437500 1.128842e+00 1.128322e+00 5.197056e-04 136 17 8 1.000000 0.437500 1.000000e+00 1.000000e+00 0.000000e+00 137 1 9 0.000000 0.500000 0.000000e+00 0.000000e+00 0.000000e+00 138 2 9 0.062500 0.500000 2.575903e-01 2.569632e-01 6.270814e-04 139 3 9 0.125000 0.500000 5.076834e-01 5.064534e-01 1.230064e-03 140 4 9 0.187500 0.500000 7.430702e-01 7.412845e-01 1.785777e-03 141 5 9 0.250000 0.500000 9.571068e-01 9.548339e-01 2.272863e-03 142 6 9 0.312500 0.500000 1.143970e+00 1.141297e+00 2.672604e-03 143 7 9 0.375000 0.500000 1.298880e+00 1.295910e+00 2.969638e-03 144 8 9 0.437500 0.500000 1.418285e+00 1.415133e+00 3.152551e-03 145 9 9 0.500000 0.500000 1.500000e+00 1.496786e+00 3.214313e-03 146 10 9 0.562500 0.500000 1.543285e+00 1.540133e+00 3.152551e-03 147 11 9 0.625000 0.500000 1.548880e+00 1.545910e+00 2.969638e-03 148 12 9 0.687500 0.500000 1.518970e+00 1.516297e+00 2.672604e-03 149 13 9 0.750000 0.500000 1.457107e+00 1.454834e+00 2.272863e-03 150 14 9 0.812500 0.500000 1.368070e+00 1.366284e+00 1.785777e-03 151 15 9 0.875000 0.500000 1.257683e+00 1.256453e+00 1.230064e-03 152 16 9 0.937500 0.500000 1.132590e+00 1.131963e+00 6.270814e-04 153 17 9 1.000000 0.500000 1.000000e+00 1.000000e+00 0.000000e+00 154 1 10 0.000000 0.562500 0.000000e+00 0.000000e+00 0.000000e+00 155 2 10 0.062500 0.562500 2.538417e-01 2.533220e-01 5.197056e-04 156 3 10 0.125000 0.562500 5.003303e-01 4.992740e-01 1.056256e-03 157 4 10 0.187500 0.562500 7.323951e-01 7.308155e-01 1.579574e-03 158 5 10 0.250000 0.562500 9.435199e-01 9.414580e-01 2.061945e-03 159 6 10 0.312500 0.562500 1.127993e+00 1.125514e+00 2.478875e-03 160 7 10 0.375000 0.562500 1.281127e+00 1.278318e+00 2.809735e-03 161 8 10 0.437500 0.562500 1.399440e+00 1.396402e+00 3.038205e-03 162 9 10 0.500000 0.562500 1.480785e+00 1.477633e+00 3.152551e-03 163 10 10 0.562500 0.562500 1.524440e+00 1.521294e+00 3.145746e-03 164 11 10 0.625000 0.562500 1.531127e+00 1.528112e+00 3.015419e-03 165 12 10 0.687500 0.562500 1.502993e+00 1.500230e+00 2.763626e-03 166 13 10 0.750000 0.562500 1.443520e+00 1.441123e+00 2.396436e-03 167 14 10 0.812500 0.562500 1.357395e+00 1.355472e+00 1.923353e-03 168 15 10 0.875000 0.562500 1.250330e+00 1.248974e+00 1.356603e-03 169 16 10 0.937500 0.562500 1.128842e+00 1.128131e+00 7.103587e-04 170 17 10 1.000000 0.562500 1.000000e+00 1.000000e+00 0.000000e+00 171 1 11 0.000000 0.625000 0.000000e+00 0.000000e+00 0.000000e+00 172 2 11 0.062500 0.625000 2.427400e-01 2.423445e-01 3.954629e-04 173 3 11 0.125000 0.625000 4.785534e-01 4.777059e-01 8.474596e-04 174 4 11 0.187500 0.625000 7.007800e-01 6.994602e-01 1.319759e-03 175 5 11 0.250000 0.625000 9.032815e-01 9.015023e-01 1.779198e-03 176 6 11 0.312500 0.625000 1.080678e+00 1.078481e+00 2.196514e-03 177 7 11 0.375000 0.625000 1.228553e+00 1.226007e+00 2.546801e-03 178 8 11 0.437500 0.625000 1.343627e+00 1.340818e+00 2.809735e-03 179 9 11 0.500000 0.625000 1.423880e+00 1.420910e+00 2.969638e-03 180 10 11 0.562500 0.625000 1.468627e+00 1.465612e+00 3.015419e-03 181 11 11 0.625000 0.625000 1.478553e+00 1.475613e+00 2.940374e-03 182 12 11 0.687500 0.625000 1.455678e+00 1.452936e+00 2.741814e-03 183 13 11 0.750000 0.625000 1.403281e+00 1.400861e+00 2.420504e-03 184 14 11 0.812500 0.625000 1.325780e+00 1.323800e+00 1.979926e-03 185 15 11 0.875000 0.625000 1.228553e+00 1.227128e+00 1.425403e-03 186 16 11 0.937500 0.625000 1.117740e+00 1.116977e+00 7.632324e-04 187 17 11 1.000000 0.625000 1.000000e+00 1.000000e+00 0.000000e+00 188 1 12 0.000000 0.687500 0.000000e+00 0.000000e+00 0.000000e+00 189 2 12 0.062500 0.687500 2.247117e-01 2.244488e-01 2.628382e-04 190 3 12 0.125000 0.687500 4.431896e-01 4.425713e-01 6.183187e-04 191 4 12 0.187500 0.687500 6.494398e-01 6.484152e-01 1.024571e-03 192 5 12 0.250000 0.687500 8.379378e-01 8.364938e-01 1.444001e-03 193 6 12 0.312500 0.687500 1.003842e+00 1.001998e+00 1.843902e-03 194 7 12 0.375000 0.687500 1.143178e+00 1.140981e+00 2.196514e-03 195 8 12 0.437500 0.687500 1.252993e+00 1.250514e+00 2.478875e-03 196 9 12 0.500000 0.687500 1.331470e+00 1.328797e+00 2.672604e-03 197 10 12 0.562500 0.687500 1.377993e+00 1.375230e+00 2.763626e-03 198 11 12 0.625000 0.687500 1.393178e+00 1.390436e+00 2.741814e-03 199 12 12 0.687500 0.687500 1.378842e+00 1.376241e+00 2.600476e-03 200 13 12 0.750000 0.687500 1.337938e+00 1.335602e+00 2.335632e-03 201 14 12 0.812500 0.687500 1.274440e+00 1.272495e+00 1.945068e-03 202 15 12 0.875000 0.687500 1.193190e+00 1.191762e+00 1.427204e-03 203 16 12 0.937500 0.687500 1.099712e+00 1.098932e+00 7.799600e-04 204 17 12 1.000000 0.687500 1.000000e+00 1.000000e+00 0.000000e+00 205 1 13 0.000000 0.750000 0.000000e+00 0.000000e+00 0.000000e+00 206 2 13 0.062500 0.750000 2.004497e-01 2.003176e-01 1.320477e-04 207 3 13 0.125000 0.750000 3.955981e-01 3.952115e-01 3.865419e-04 208 4 13 0.187500 0.750000 5.803475e-01 5.796313e-01 7.161482e-04 209 5 13 0.250000 0.750000 7.500000e-01 7.489199e-01 1.080089e-03 210 6 13 0.312500 0.750000 9.004378e-01 8.989938e-01 1.444001e-03 211 7 13 0.375000 0.750000 1.028281e+00 1.026502e+00 1.779198e-03 212 8 13 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