07-Jan-2022 19:58:15 fem1d_adaptive_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test fem1d_adaptive(). 07-Jan-2022 19:58:15 FEM1D_ADAPTIVE MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Solve the two-point boundary value problem: -d/dx ( P(x) * dU(x)/dx ) + Q(x) * U(x) = F(x) on the interval [0,1], specifying the value of U at each endpoint. The number of basis functions per element is 2 The number of quadrature points per element is 2 Problem index = 6 "ARCTAN" problem: U(X) = ATAN((X-0.5)/A) P(X) = 1.0 Q(X) = 0.0 F(X) = 2*A*(X-0.5)/(A^2+(X-0.5)^2)^2 IBC = 3 UL = ATAN(-0.5/A) UR = ATAN( 0.5/A) A = 0.010000 Arctangent problem The equation is to be solved for X greater than 0.000000 and less than 1.000000 The boundary conditions are: At X = XL, U = -1.550799 At X = XR, U = 1.550799 Begin new iteration with 4 nodes. Printout of tridiagonal linear system: Equation A-Left A-Diag A-Rite RHS 1 8.000000 -4.000000 -9.875060 2 -4.000000 8.000000 -4.000000 0.000000 3 -4.000000 8.000000 9.875060 Basic solution Node X(I) U(X(I)) Uexact Error 0 0.000000 -1.550799 -1.550799 0.000000 1 0.250000 -1.234382 -1.530818 0.296435 2 0.500000 -0.000000 0.000000 -0.000000 3 0.750000 1.234382 1.530818 -0.296435 4 1.000000 1.550799 1.550799 0.000000 ETA 0.244233 2.196335 2.196335 0.244233 Tolerance = 1.464351 Subdivide interval 2 Subdivide interval 3 Begin new iteration with 6 nodes. Basic solution Node X(I) U(X(I)) Uexact Error 0 0.000000 -1.550799 -1.550799 0.000000 1 0.250000 -1.572694 -1.530818 -0.041876 2 0.375000 -1.553638 -1.490966 -0.062671 3 0.500000 -0.000000 0.000000 -0.000000 4 0.625000 1.553638 1.490966 0.062671 5 0.750000 1.572694 1.530818 0.041876 6 1.000000 1.550799 1.550799 0.000000 ETA 0.009444 0.185938 3.526846 3.526846 0.185938 0.009444 Tolerance = 1.488901 Subdivide interval 3 Subdivide interval 4 Begin new iteration with 8 nodes. Basic solution Node X(I) U(X(I)) Uexact Error 0 0.000000 -1.550799 -1.550799 0.000000 1 0.250000 -1.744159 -1.530818 -0.213342 2 0.375000 -1.810836 -1.490966 -0.319870 3 0.437500 -1.785029 -1.412141 -0.372888 4 0.500000 -0.000000 0.000000 -0.000000 5 0.562500 1.785029 1.412141 0.372888 6 0.625000 1.810836 1.490966 0.319870 7 0.750000 1.744159 1.530818 0.213342 8 1.000000 1.550799 1.550799 0.000000 ETA 0.009444 0.026573 0.292454 3.343300 3.343300 0.292454 0.026573 0.009444 Tolerance = 1.101541 Subdivide interval 4 Subdivide interval 5 Begin new iteration with 10 nodes. Basic solution Node X(I) U(X(I)) Uexact Error 0 0.000000 -1.550799 -1.550799 0.000000 1 0.250000 -1.564034 -1.530818 -0.033217 2 0.375000 -1.540648 -1.490966 -0.049682 3 0.437500 -1.469810 -1.412141 -0.057669 4 0.468750 -1.322539 -1.261093 -0.061446 5 0.500000 0.000000 0.000000 0.000000 6 0.531250 1.322539 1.261093 0.061446 7 0.562500 1.469810 1.412141 0.057669 8 0.625000 1.540648 1.490966 0.049682 9 0.750000 1.564034 1.530818 0.033217 10 1.000000 1.550799 1.550799 0.000000 ETA 0.009444 0.026573 0.073637 0.235021 2.822379 2.822379 0.235021 0.073637 0.026573 0.009444 Tolerance = 0.760103 Subdivide interval 5 Subdivide interval 6 Begin new iteration with 12 nodes. Basic solution Node X(I) U(X(I)) Uexact Error 0 0.000000 -1.550799 -1.550799 0.000000 1 0.250000 -1.512161 -1.530818 0.018657 2 0.375000 -1.462838 -1.490966 0.028128 3 0.437500 -1.379032 -1.412141 0.033109 4 0.468750 -1.225277 -1.261093 0.035817 5 0.484375 -0.964992 -1.001483 0.036491 6 0.500000 0.000000 0.000000 0.000000 7 0.515625 0.964992 1.001483 -0.036491 8 0.531250 1.225277 1.261093 -0.035817 9 0.562500 1.379032 1.412141 -0.033109 10 0.625000 1.462838 1.490966 -0.028128 11 0.750000 1.512161 1.530818 -0.018657 12 1.000000 1.550799 1.550799 0.000000 ETA 0.009444 0.026573 0.073637 0.192415 0.416090 1.831096 1.831096 0.416090 0.192415 0.073637 0.026573 0.009444 Tolerance = 0.509861 Subdivide interval 6 Subdivide interval 7 Begin new iteration with 14 nodes. Basic solution Node X(I) U(X(I)) Uexact Error 0 0.000000 -1.550799 -1.550799 0.000000 1 0.250000 -1.528725 -1.530818 0.002092 2 0.375000 -1.487685 -1.490966 0.003282 3 0.437500 -1.408019 -1.412141 0.004122 4 0.468750 -1.256334 -1.261093 0.004759 5 0.484375 -0.997085 -1.001483 0.004398 6 0.492188 -0.660270 -0.663203 0.002933 7 0.500000 0.000000 0.000000 0.000000 8 0.507812 0.660270 0.663203 -0.002933 9 0.515625 0.997085 1.001483 -0.004398 10 0.531250 1.256334 1.261093 -0.004759 11 0.562500 1.408019 1.412141 -0.004122 12 0.625000 1.487685 1.490966 -0.003282 13 0.750000 1.528725 1.530818 -0.002092 14 1.000000 1.550799 1.550799 0.000000 ETA 0.009444 0.026573 0.073637 0.192415 0.410124 0.512307 0.653928 0.653928 0.512307 0.410124 0.192415 0.073637 0.026573 0.009444 Tolerance = 0.322026 Subdivide interval 5 Subdivide interval 6 Subdivide interval 7 Subdivide interval 8 Subdivide interval 9 Subdivide interval 10 Begin new iteration with 20 nodes. Basic solution Node X(I) U(X(I)) Uexact Error 0 0.000000 -1.550799 -1.550799 0.000000 1 0.250000 -1.529415 -1.530818 0.001403 2 0.375000 -1.488719 -1.490966 0.002247 3 0.437500 -1.409226 -1.412141 0.002915 4 0.468750 -1.257628 -1.261093 0.003466 5 0.476562 -1.164900 -1.167515 0.002615 6 0.484375 -0.999675 -1.001483 0.001808 7 0.488281 -0.863012 -0.864370 0.001358 8 0.492188 -0.662316 -0.663203 0.000887 9 0.496094 -0.372028 -0.372398 0.000371 10 0.500000 -0.000000 0.000000 -0.000000 11 0.503906 0.372028 0.372398 -0.000371 12 0.507812 0.662316 0.663203 -0.000887 13 0.511719 0.863012 0.864370 -0.001358 14 0.515625 0.999675 1.001483 -0.001808 15 0.523438 1.164900 1.167515 -0.002615 16 0.531250 1.257628 1.261093 -0.003466 17 0.562500 1.409226 1.412141 -0.002915 18 0.625000 1.488719 1.490966 -0.002247 19 0.750000 1.529415 1.530818 -0.001403 20 1.000000 1.550799 1.550799 0.000000 ETA 0.009444 0.026573 0.073637 0.192422 0.094285 0.209540 0.143922 0.220710 0.276384 0.151308 0.151308 0.276384 0.220710 0.143922 0.209540 0.094285 0.192422 0.073637 0.026573 0.009444 Tolerance = 0.167797 Subdivide interval 4 Subdivide interval 6 Subdivide interval 8 Subdivide interval 9 Subdivide interval 12 Subdivide interval 13 Subdivide interval 15 Subdivide interval 17 Begin new iteration with 28 nodes. Basic solution Node X(I) U(X(I)) Uexact Error 0 0.000000 -1.550799 -1.550799 0.000000 1 0.250000 -1.529819 -1.530818 0.000999 2 0.375000 -1.489325 -1.490966 0.001641 3 0.437500 -1.409933 -1.412141 0.002208 4 0.453125 -1.358934 -1.360614 0.001680 5 0.468750 -1.259832 -1.261093 0.001261 6 0.476562 -1.166560 -1.167515 0.000954 7 0.480469 -1.096809 -1.097595 0.000785 8 0.484375 -1.000866 -1.001483 0.000617 9 0.488281 -0.863924 -0.864370 0.000447 10 0.490234 -0.773179 -0.773541 0.000362 11 0.492188 -0.662927 -0.663203 0.000276 12 0.494141 -0.529825 -0.530015 0.000190 13 0.496094 -0.372295 -0.372398 0.000104 14 0.500000 -0.000000 0.000000 -0.000000 15 0.503906 0.372295 0.372398 -0.000104 16 0.505859 0.529825 0.530015 -0.000190 17 0.507812 0.662927 0.663203 -0.000276 18 0.509766 0.773179 0.773541 -0.000362 19 0.511719 0.863924 0.864370 -0.000447 20 0.515625 1.000866 1.001483 -0.000617 21 0.519531 1.096809 1.097595 -0.000785 22 0.523438 1.166560 1.167515 -0.000954 23 0.531250 1.259832 1.261093 -0.001261 24 0.546875 1.358934 1.360614 -0.001680 25 0.562500 1.409933 1.412141 -0.002208 26 0.625000 1.489325 1.490966 -0.001641 27 0.750000 1.529819 1.530818 -0.000999 28 1.000000 1.550799 1.550799 0.000000 ETA 0.009444 0.026573 0.073643 0.040325 0.105528 0.094199 0.059061 0.091140 0.143922 0.070682 0.085315 0.096668 0.096701 0.151307 0.151307 0.096701 0.096668 0.085315 0.070682 0.143922 0.091140 0.059061 0.094199 0.105528 0.040325 0.073643 0.026573 0.009444 Tolerance = 0.098110 Subdivide interval 5 Subdivide interval 9 Subdivide interval 14 Subdivide interval 15 Subdivide interval 20 Subdivide interval 24 The iterations did not reach their goal. The next value of N is 34 which exceeds NMAX = 30 FEM1D_ADAPTIVE: Normal end of execution. 07-Jan-2022 19:58:15 fem1d_adaptive_test(): Normal end of execution. 07-Jan-2022 19:58:15