29 April 2007 8:22:14.000 AM FEM1D_ADAPTIVE FORTRAN77 version Solve the two-point boundary value problem: -d/dx P du/dx + Q U = F on the interval [0,1], specifying the value of U or 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 = 0.100000E-01 Arctangent problem The equation is to be solved for X greater than 0. and less than 1. The boundary conditions are: At X = XL, U = -1.55079899 At X = XR, U = 1.55079899 Begin new iteration with 4 nodes. Printout of tridiagonal linear system: Equation A-Left A-Diag A-Rite RHS 1 8.00000 -4.00000 -9.87506 2 -4.00000 8.00000 -4.00000 0.138778E-15 3 -4.00000 8.00000 9.87506 Basic solution Node X(I) U(X(I)) U exact Error 0 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.23438 -1.53082 0.296435 2 0.500000 -0.555112E-15 0.00000 -0.555112E-15 3 0.750000 1.23438 1.53082 -0.296435 4 1.00000 1.55080 1.55080 0.00000 ETA 0.2442334 2.19633473 2.19633473 0.2442334 Tolerance = 1.46435088 Subdivide interval 2 Subdivide interval 3 Begin new iteration with 6 nodes. Basic solution Node X(I) U(X(I)) U exact Error 0 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.57269 -1.53082 -0.418763E-01 2 0.375000 -1.55364 -1.49097 -0.626714E-01 3 0.500000 -0.655032E-13 0.00000 -0.655032E-13 4 0.625000 1.55364 1.49097 0.626714E-01 5 0.750000 1.57269 1.53082 0.418763E-01 6 1.00000 1.55080 1.55080 0.00000 ETA 0.00944353343 0.185937581 3.526846 3.526846 0.185937581 0.00944353343 Tolerance = 1.48890085 Subdivide interval 3 Subdivide interval 4 Begin new iteration with 8 nodes. Basic solution Node X(I) U(X(I)) U exact Error 0 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.74416 -1.53082 -0.213342 2 0.375000 -1.81084 -1.49097 -0.319870 3 0.437500 -1.78503 -1.41214 -0.372888 4 0.500000 -0.244249E-14 0.00000 -0.244249E-14 5 0.562500 1.78503 1.41214 0.372888 6 0.625000 1.81084 1.49097 0.319870 7 0.750000 1.74416 1.53082 0.213342 8 1.00000 1.55080 1.55080 0.00000 ETA 0.00944353343 0.0265730457 0.292454403 3.34330049 3.34330049 0.292454403 0.0265730457 0.00944353343 Tolerance = 1.10154144 Subdivide interval 4 Subdivide interval 5 Begin new iteration with 10 nodes. Basic solution Node X(I) U(X(I)) U exact Error 0 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.56403 -1.53082 -0.332166E-01 2 0.375000 -1.54065 -1.49097 -0.496819E-01 3 0.437500 -1.46981 -1.41214 -0.576689E-01 4 0.468750 -1.32254 -1.26109 -0.614455E-01 5 0.500000 0.688338E-13 0.00000 0.688338E-13 6 0.531250 1.32254 1.26109 0.614455E-01 7 0.562500 1.46981 1.41214 0.576689E-01 8 0.625000 1.54065 1.49097 0.496819E-01 9 0.750000 1.56403 1.53082 0.332166E-01 10 1.00000 1.55080 1.55080 0.00000 ETA 0.00944353343 0.0265730457 0.0736369485 0.235020653 2.82237926 2.82237926 0.235020653 0.0736369485 0.0265730457 0.00944353343 Tolerance = 0.760102826 Subdivide interval 5 Subdivide interval 6 Begin new iteration with 12 nodes. Basic solution Node X(I) U(X(I)) U exact Error 0 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.51216 -1.53082 0.186565E-01 2 0.375000 -1.46284 -1.49097 0.281279E-01 3 0.437500 -1.37903 -1.41214 0.331091E-01 4 0.468750 -1.22528 -1.26109 0.358167E-01 5 0.484375 -0.964992 -1.00148 0.364909E-01 6 0.500000 0.455191E-13 0.00000 0.455191E-13 7 0.515625 0.964992 1.00148 -0.364909E-01 8 0.531250 1.22528 1.26109 -0.358167E-01 9 0.562500 1.37903 1.41214 -0.331091E-01 10 0.625000 1.46284 1.49097 -0.281279E-01 11 0.750000 1.51216 1.53082 -0.186565E-01 12 1.00000 1.55080 1.55080 0.00000 ETA 0.00944353343 0.0265730457 0.0736369485 0.192414859 0.416090219 1.83109612 1.83109612 0.416090219 0.192414859 0.0736369485 0.0265730457 0.00944353343 Tolerance = 0.509860945 Subdivide interval 6 Subdivide interval 7 Begin new iteration with 14 nodes. Basic solution Node X(I) U(X(I)) U exact Error 0 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.52873 -1.53082 0.209243E-02 2 0.375000 -1.48768 -1.49097 0.328175E-02 3 0.437500 -1.40802 -1.41214 0.412196E-02 4 0.468750 -1.25633 -1.26109 0.475898E-02 5 0.484375 -0.997085 -1.00148 0.439793E-02 6 0.492188 -0.660270 -0.663203 0.293290E-02 7 0.500000 0.208722E-13 0.00000 0.208722E-13 8 0.507812 0.660270 0.663203 -0.293290E-02 9 0.515625 0.997085 1.00148 -0.439793E-02 10 0.531250 1.25633 1.26109 -0.475898E-02 11 0.562500 1.40802 1.41214 -0.412196E-02 12 0.625000 1.48768 1.49097 -0.328175E-02 13 0.750000 1.52873 1.53082 -0.209243E-02 14 1.00000 1.55080 1.55080 0.00000 ETA 0.00944353343 0.0265730457 0.0736369485 0.192414859 0.410124159 0.512306954 0.653928074 0.653928074 0.512306954 0.410124159 0.192414859 0.0736369485 0.0265730457 0.00944353343 Tolerance = 0.322026155 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)) U exact Error 0 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.52941 -1.53082 0.140268E-02 2 0.375000 -1.48872 -1.49097 0.224713E-02 3 0.437500 -1.40923 -1.41214 0.291490E-02 4 0.468750 -1.25763 -1.26109 0.346570E-02 5 0.476562 -1.16490 -1.16751 0.261453E-02 6 0.484375 -0.999675 -1.00148 0.180788E-02 7 0.488281 -0.863012 -0.864370 0.135779E-02 8 0.492188 -0.662316 -0.663203 0.886981E-03 9 0.496094 -0.372028 -0.372398 0.370799E-03 10 0.500000 -0.344724E-13 0.00000 -0.344724E-13 11 0.503906 0.372028 0.372398 -0.370799E-03 12 0.507812 0.662316 0.663203 -0.886981E-03 13 0.511719 0.863012 0.864370 -0.135779E-02 14 0.515625 0.999675 1.00148 -0.180788E-02 15 0.523438 1.16490 1.16751 -0.261453E-02 16 0.531250 1.25763 1.26109 -0.346570E-02 17 0.562500 1.40923 1.41214 -0.291490E-02 18 0.625000 1.48872 1.49097 -0.224713E-02 19 0.750000 1.52941 1.53082 -0.140268E-02 20 1.00000 1.55080 1.55080 0.00000 ETA 0.00944353343 0.0265730457 0.0736369485 0.192422343 0.0942853749 0.20953993 0.143921875 0.220709516 0.276383751 0.151307984 0.151307984 0.276383751 0.220709516 0.143921875 0.20953993 0.0942853749 0.192422343 0.0736369485 0.0265730457 0.00944353343 Tolerance = 0.167796916 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)) U exact Error 0 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.52982 -1.53082 0.998794E-03 2 0.375000 -1.48933 -1.49097 0.164130E-02 3 0.437500 -1.40993 -1.41214 0.220810E-02 4 0.453125 -1.35893 -1.36061 0.167961E-02 5 0.468750 -1.25983 -1.26109 0.126092E-02 6 0.476562 -1.16656 -1.16751 0.954394E-03 7 0.480469 -1.09681 -1.09759 0.785440E-03 8 0.484375 -1.00087 -1.00148 0.617209E-03 9 0.488281 -0.863924 -0.864370 0.446597E-03 10 0.490234 -0.773179 -0.773541 0.361764E-03 11 0.492188 -0.662927 -0.663203 0.276314E-03 12 0.494141 -0.529825 -0.530015 0.190069E-03 13 0.496094 -0.372295 -0.372398 0.103811E-03 14 0.500000 -0.500711E-13 0.00000 -0.500711E-13 15 0.503906 0.372295 0.372398 -0.103811E-03 16 0.505859 0.529825 0.530015 -0.190069E-03 17 0.507812 0.662927 0.663203 -0.276314E-03 18 0.509766 0.773179 0.773541 -0.361764E-03 19 0.511719 0.863924 0.864370 -0.446597E-03 20 0.515625 1.00087 1.00148 -0.617209E-03 21 0.519531 1.09681 1.09759 -0.785440E-03 22 0.523438 1.16656 1.16751 -0.954394E-03 23 0.531250 1.25983 1.26109 -0.126092E-02 24 0.546875 1.35893 1.36061 -0.167961E-02 25 0.562500 1.40993 1.41214 -0.220810E-02 26 0.625000 1.48933 1.49097 -0.164130E-02 27 0.750000 1.52982 1.53082 -0.998794E-03 28 1.00000 1.55080 1.55080 0.00000 ETA 0.00944353343 0.0265730457 0.0736427257 0.0403251388 0.10552752 0.0941990542 0.0590606433 0.0911395224 0.143921664 0.0706817241 0.085315287 0.0966675038 0.0967009134 0.151307088 0.151307088 0.0967009134 0.0966675038 0.085315287 0.0706817241 0.143921664 0.0911395224 0.0590606433 0.0941990542 0.10552752 0.0403251388 0.0736427257 0.0265730457 0.00944353343 Tolerance = 0.0981104597 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. 29 April 2007 8:22:14.000 AM