June 24 2002 11:02:06.252 AM ADAPT 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 at each endpoint. The number of basis functions per element is 2 The number of quadrature points per element is 2 Arctangent problem The equation is to be solved for X greater than 0.E+0 and less than 1. The boundary conditions are: At X = XL, U= -1.55079901 At X = XR, U= 1.55079901 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 -0.201166E-06 3 -4.00000 8.00000 9.87506 Basic solution Node X(I) U(X(I)) Uexact Error 0 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.23438 -1.53082 0.296435 2 0.500000 0.178814E-06 0.00000 0.178814E-06 3 0.750000 1.23438 1.53082 -0.296435 4 1.00000 1.55080 1.55080 0.00000 ETA 0.244233504 2.19633579 2.19633865 0.24423416 Tolerance = 1.46435273 Subdivide interval 2 Subdivide interval 3 Begin new iteration with 6 nodes. Basic solution Node X(I) U(X(I)) Uexact Error 0 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.57268 -1.53082 -0.418588E-01 2 0.375000 -1.55361 -1.49097 -0.626451E-01 3 0.500000 0.357628E-04 0.00000 0.357628E-04 4 0.625000 1.55367 1.49097 0.627003E-01 5 0.750000 1.57271 1.53082 0.418956E-01 6 1.00000 1.55080 1.55080 0.00000 ETA 9.443454444E-3 0.185937747 3.52684832 3.52684784 0.185936674 9.443540126E-3 Tolerance = 1.48890162 Subdivide interval 3 Subdivide interval 4 Begin new iteration with 8 nodes. Basic solution Node X(I) U(X(I)) Uexact Error 0 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.74416 -1.53082 -0.213344 2 0.375000 -1.81084 -1.49097 -0.319872 3 0.437500 -1.78503 -1.41214 -0.372891 4 0.500000 -0.178814E-05 0.00000 -0.178814E-05 5 0.562500 1.78503 1.41214 0.372887 6 0.625000 1.81084 1.49097 0.319869 7 0.750000 1.74416 1.53082 0.213341 8 1.00000 1.55080 1.55080 0.00000 ETA 9.443454444E-3 2.657303214E-2 0.292455763 3.34329844 3.34329748 0.292455763 2.657315321E-2 9.443454444E-3 Tolerance = 1.10154104 Subdivide interval 4 Subdivide interval 5 Begin new iteration with 10 nodes. Basic solution Node X(I) U(X(I)) Uexact Error 0 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.56404 -1.53082 -0.332178E-01 2 0.375000 -1.54065 -1.49097 -0.496833E-01 3 0.437500 -1.46981 -1.41214 -0.576706E-01 4 0.468750 -1.32254 -1.26109 -0.614473E-01 5 0.500000 -0.250340E-05 0.00000 -0.250340E-05 6 0.531250 1.32254 1.26109 0.614423E-01 7 0.562500 1.46981 1.41214 0.576658E-01 8 0.625000 1.54065 1.49097 0.496793E-01 9 0.750000 1.56403 1.53082 0.332149E-01 10 1.00000 1.55080 1.55080 0.00000 ETA 9.443285875E-3 2.657279372E-2 7.363697886E-2 0.235020936 2.82237816 2.82238293 0.235019565 7.363715768E-2 2.657315135E-2 9.443454444E-3 Tolerance = 0.760103047 Subdivide interval 5 Subdivide interval 6 Begin new iteration with 12 nodes. Basic solution Node X(I) U(X(I)) Uexact Error 0 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.51213 -1.53082 0.186905E-01 2 0.375000 -1.46279 -1.49097 0.281789E-01 3 0.437500 -1.37897 -1.41214 0.331687E-01 4 0.468750 -1.22521 -1.26109 0.358804E-01 5 0.484375 -0.964926 -1.00148 0.365568E-01 6 0.500000 0.679493E-04 0.00000 0.679493E-04 7 0.515625 0.965059 1.00148 -0.364239E-01 8 0.531250 1.22534 1.26109 -0.357516E-01 9 0.562500 1.37909 1.41214 -0.330485E-01 10 0.625000 1.46289 1.49097 -0.280759E-01 11 0.750000 1.51220 1.53082 -0.186219E-01 12 1.00000 1.55080 1.55080 0.00000 ETA 9.443454444E-3 2.657291293E-2 7.363681495E-2 0.192414939 0.416090488 1.83110094 1.83109522 0.416089982 0.192415178 7.363732159E-2 2.657303214E-2 9.443537332E-3 Tolerance = 0.509861469 Subdivide interval 6 Subdivide interval 7 Begin new iteration with 14 nodes. Basic solution Node X(I) U(X(I)) Uexact Error 0 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.52874 -1.53082 0.207603E-02 2 0.375000 -1.48771 -1.49097 0.325727E-02 3 0.437500 -1.40805 -1.41214 0.409341E-02 4 0.468750 -1.25636 -1.26109 0.472844E-02 5 0.484375 -0.997117 -1.00148 0.436634E-02 6 0.492187 -0.660302 -0.663203 0.290060E-02 7 0.500000 -0.322461E-04 0.00000 -0.322461E-04 8 0.507812 0.660238 0.663203 -0.296509E-02 9 0.515625 0.997053 1.00148 -0.442976E-02 10 0.531250 1.25630 1.26109 -0.478959E-02 11 0.562500 1.40799 1.41214 -0.415063E-02 12 0.625000 1.48766 1.49097 -0.330639E-02 13 0.750000 1.52871 1.53082 -0.210881E-02 14 1.00000 1.55080 1.55080 0.00000 ETA 9.443454444E-3 2.657279372E-2 7.363697886E-2 0.192414701 0.410124213 0.512306094 0.653930008 0.653927863 0.512302279 0.410123855 0.192415178 7.363715023E-2 2.657291293E-2 9.443540126E-3 Tolerance = 0.322025806 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 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.52944 -1.53082 0.137389E-02 2 0.375000 -1.48876 -1.49097 0.220394E-02 3 0.437500 -1.40928 -1.41214 0.286460E-02 4 0.468750 -1.25768 -1.26109 0.341189E-02 5 0.476562 -1.16495 -1.16751 0.255990E-02 6 0.484375 -0.999731 -1.00148 0.175250E-02 7 0.488281 -0.863068 -0.864370 0.130206E-02 8 0.492187 -0.662372 -0.663203 0.830710E-03 9 0.496094 -0.372085 -0.372398 0.313729E-03 10 0.500000 -0.575781E-04 0.00000 -0.575781E-04 11 0.503906 0.371970 0.372398 -0.428885E-03 12 0.507812 0.662257 0.663203 -0.945568E-03 13 0.511719 0.862954 0.864370 -0.141627E-02 14 0.515625 0.999618 1.00148 -0.186551E-02 15 0.523437 1.16484 1.16751 -0.267112E-02 16 0.531250 1.25757 1.26109 -0.352144E-02 17 0.562500 1.40917 1.41214 -0.296688E-02 18 0.625000 1.48867 1.49097 -0.229156E-02 19 0.750000 1.52939 1.53082 -0.143230E-02 20 1.00000 1.55080 1.55080 0.00000 ETA 9.443285875E-3 2.657279372E-2 7.363681495E-2 0.192422181 9.428463876E-2 0.209540933 0.143921584 0.220707297 0.276383936 0.151309788 0.151311636 0.276384294 0.220702231 0.143922254 0.209543556 9.428565204E-2 0.19242242 7.363681495E-2 2.657315321E-2 9.443285875E-3 Tolerance = 0.16779691 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 0.00000 -1.55080 -1.55080 0.00000 1 0.250000 -1.52985 -1.53082 0.964999E-03 2 0.375000 -1.48938 -1.49097 0.159073E-02 3 0.437500 -1.40999 -1.41214 0.214911E-02 4 0.453125 -1.35900 -1.36061 0.161850E-02 5 0.468750 -1.25990 -1.26109 0.119781E-02 6 0.476562 -1.16662 -1.16751 0.890136E-03 7 0.480469 -1.09687 -1.09759 0.720620E-03 8 0.484375 -1.00093 -1.00148 0.551820E-03 9 0.488281 -0.863990 -0.864370 0.380695E-03 10 0.490234 -0.773245 -0.773541 0.295639E-03 11 0.492187 -0.662993 -0.663203 0.209808E-03 12 0.494141 -0.529892 -0.530015 0.123262E-03 13 0.496094 -0.372362 -0.372398 0.368357E-04 14 0.500000 -0.674725E-04 0.00000 -0.674725E-04 15 0.503906 0.372227 0.372398 -0.171781E-03 16 0.505859 0.529757 0.530015 -0.257909E-03 17 0.507812 0.662859 0.663203 -0.344098E-03 18 0.509766 0.773111 0.773541 -0.429809E-03 19 0.511719 0.863856 0.864370 -0.514269E-03 20 0.515625 1.00080 1.00148 -0.684023E-03 21 0.519531 1.09674 1.09759 -0.851512E-03 22 0.523437 1.16649 1.16751 -0.102007E-02 23 0.531250 1.25977 1.26109 -0.132561E-02 24 0.546875 1.35887 1.36061 -0.174201E-02 25 0.562500 1.40987 1.41214 -0.226831E-02 26 0.625000 1.48927 1.49097 -0.169289E-02 27 0.750000 1.52978 1.53082 -0.103319E-02 28 1.00000 1.55080 1.55080 0.00000 ETA 9.443454444E-3 2.657279372E-2 7.36425966E-2 4.032479599E-2 0.105527408 9.419885278E-2 5.90589121E-2 9.114171565E-2 0.143922716 7.068157196E-2 8.531570435E-2 9.666967392E-2 9.669930488E-2 0.151308805 0.151310831 9.669810534E-2 9.666824341E-2 8.531618118E-2 7.068252563E-2 0.14392069 9.114104509E-2 5.906228721E-2 9.419885278E-2 0.105528086 4.032544419E-2 7.364292443E-2 2.657315321E-2 9.443454444E-3 Tolerance = 9.811087698E-2 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