fem2d_project_function_output.txt

FEM2D_LEASTSQUARES
  C++ version

  Seek U(x,y), the solution of the least squares equation:

  Minimize L2 norm of U(x,y) - W(x,y), for W(x,y) given,
  with U(x,y) a piecewise linear function in the interior,
  and matching W(x,y) on the boundary.

  Reformulate this in terms of a finite element problem:

  ( U(x,y) - W(x,y), V(x,y) ) = 0 inside the region,
    U(x,y)                    = W(x,y) on the boundary

  The region is a rectangle, defined by:

  0 = XL<= X <= XR = 1
  0 = YB<= Y <= YT = 1

  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(x,y)          W(x,y)

     0     1     1           0           0               0               0               0
     1     2     1      0.0625           0          0.0625          0.0625               0
     2     3     1       0.125           0           0.125           0.125               0
     3     4     1      0.1875           0          0.1875          0.1875               0
     4     5     1        0.25           0            0.25            0.25               0
     5     6     1      0.3125           0          0.3125          0.3125               0
     6     7     1       0.375           0           0.375           0.375               0
     7     8     1      0.4375           0          0.4375          0.4375               0
     8     9     1         0.5           0             0.5             0.5               0
     9    10     1      0.5625           0          0.5625          0.5625               0
    10    11     1       0.625           0           0.625           0.625               0
    11    12     1      0.6875           0          0.6875          0.6875               0
    12    13     1        0.75           0            0.75            0.75               0
    13    14     1      0.8125           0          0.8125          0.8125               0
    14    15     1       0.875           0           0.875           0.875               0
    15    16     1      0.9375           0          0.9375          0.9375               0
    16    17     1           1           0               1               1               0

    17     1     2           0      0.0625               0               0               0
    18     2     2      0.0625      0.0625         0.10579         0.10056      0.00522933
    19     3     2       0.125      0.0625        0.203545        0.199658      0.00388708
    20     4     2      0.1875      0.0625        0.299951        0.295886      0.00406452
    21     5     2        0.25      0.0625        0.391603         0.38795      0.00365301
    22     6     2      0.3125      0.0625        0.477924        0.474712      0.00321207
    23     7     2       0.375      0.0625         0.55786         0.55524      0.00261959
    24     8     2      0.4375      0.0625        0.630775        0.628842      0.00193347
    25     9     2         0.5      0.0625        0.696262         0.69509      0.00117132
    26    10     2      0.5625      0.0625        0.754206        0.753842     0.000364567
    27    11     2       0.625      0.0625        0.804784         0.80524     0.000456313
    28    12     2      0.6875      0.0625        0.848452        0.849712       0.0012595
    29    13     2        0.75      0.0625        0.885935         0.88795      0.00201456
    30    14     2      0.8125      0.0625         0.91819        0.920886      0.00269655
    31    15     2       0.875      0.0625        0.946453        0.949658      0.00320434
    32    16     2      0.9375      0.0625        0.971294         0.97556      0.00426653
    33    17     2           1      0.0625               1               1               0

    34     1     3           0       0.125               0               0               0
    35     2     3      0.0625       0.125        0.141045        0.137158      0.00388708
    36     3     3       0.125       0.125        0.274772        0.271447      0.00332555
    37     4     3      0.1875       0.125        0.403832        0.400108       0.0037244
    38     5     3        0.25       0.125        0.524307        0.520598      0.00370845
    39     6     3      0.3125       0.125        0.634306         0.63069      0.00361675
    40     7     3       0.375       0.125        0.731923        0.728553      0.00336996
    41     8     3      0.4375       0.125        0.815828         0.81283      0.00299745
    42     9     3         0.5       0.125        0.885192        0.882683      0.00250889
    43    10     3      0.5625       0.125        0.939754         0.93783      0.00192411
    44    11     3       0.625       0.125        0.979819        0.978553      0.00126534
    45    12     3      0.6875       0.125         1.00625         1.00569     0.000557444
    46    13     3        0.75       0.125         1.02043          1.0206      0.00016549
    47    14     3      0.8125       0.125         1.02417         1.02511     0.000932687
    48    15     3       0.875       0.125         1.02009         1.02145        0.001355
    49    16     3      0.9375       0.125         1.00895         1.01216      0.00320434
    50    17     3           1       0.125               1               1               0

    51     1     4           0      0.1875               0               0               0
    52     2     4      0.0625      0.1875        0.174951        0.170886      0.00406452
    53     3     4       0.125      0.1875        0.341332        0.337608       0.0037244
    54     4     4      0.1875      0.1875        0.500453        0.496158      0.00429513
    55     5     4        0.25      0.1875        0.647291        0.642847      0.00444373
    56     6     4      0.3125      0.1875        0.778923         0.77444      0.00448298
    57     7     4       0.375      0.1875        0.892616         0.88828      0.00433565
    58     8     4      0.4375      0.1875         0.98642        0.982395      0.00402493
    59     9     4         0.5      0.1875         1.05913         1.05557      0.00355884
    60    10     4      0.5625      0.1875         1.11035          1.1074      0.00295607
    61    11     4       0.625      0.1875         1.14052         1.13828      0.00224019
    62    12     4      0.6875      0.1875         1.15087         1.14944      0.00143454
    63    13     4        0.75      0.1875         1.14344         1.14285      0.00059487
    64    14     4      0.8125      0.1875         1.12079         1.12116     0.000366704
    65    15     4       0.875      0.1875         1.08667         1.08761     0.000932687
    66    16     4      0.9375      0.1875         1.04319         1.04589      0.00269655
    67    17     4           1      0.1875               1               1               0

    68     1     5           0        0.25               0               0               0
    69     2     5      0.0625        0.25        0.204103         0.20045      0.00365301
    70     3     5       0.125        0.25        0.399307        0.395598      0.00370845
    71     4     5      0.1875        0.25        0.584791        0.580347      0.00444373
    72     5     5        0.25        0.25        0.754818            0.75      0.00481787
    73     6     5      0.3125        0.25        0.905487        0.900438      0.00504935
    74     7     5       0.375        0.25         1.03336         1.02828       0.0050778
    75     8     5      0.4375        0.25         1.13593         1.13102      0.00491285
    76     9     5         0.5        0.25         1.21167         1.20711      0.00455886
    77    10     5      0.5625        0.25         1.26005         1.25602      0.00402943
    78    11     5       0.625        0.25         1.28163         1.27828      0.00334663
    79    12     5      0.6875        0.25         1.27797         1.27544      0.00252838
    80    13     5        0.75        0.25         1.25164            1.25      0.00164007
    81    14     5      0.8125        0.25         1.20594         1.20535      0.00059487
    82    15     5       0.875        0.25         1.14543          1.1456      0.00016549
    83    16     5      0.9375        0.25         1.07344         1.07545      0.00201456
    84    17     5           1        0.25               1               1               0

    85     1     6           0      0.3125               0               0               0
    86     2     6      0.0625      0.3125        0.227924        0.224712      0.00321207
    87     3     6       0.125      0.3125        0.446806         0.44319      0.00361675
    88     4     6      0.1875      0.3125        0.653923         0.64944      0.00448298
    89     5     6        0.25      0.3125        0.842987        0.837938      0.00504935
    90     6     6      0.3125      0.3125         1.00929         1.00384      0.00544661
    91     7     6       0.375      0.3125         1.14881         1.14318      0.00563042
    92     8     6      0.4375      0.3125         1.25859         1.25299      0.00559825
    93     9     6         0.5      0.3125         1.33682         1.33147      0.00535113
    94    10     6      0.5625      0.3125         1.38289         1.37799      0.00489781
    95    11     6       0.625      0.3125         1.39744         1.39318      0.00425823
    96    12     6      0.6875      0.3125         1.38229         1.37884      0.00344814
    97    13     6        0.75      0.3125         1.34047         1.33794      0.00252838
    98    14     6      0.8125      0.3125         1.27587         1.27444      0.00143454
    99    15     6       0.875      0.3125         1.19375         1.19319     0.000557444
   100    16     6      0.9375      0.3125         1.09845         1.09971       0.0012595
   101    17     6           1      0.3125               1               1               0

   102     1     7           0       0.375               0               0               0
   103     2     7      0.0625       0.375         0.24536         0.24274      0.00261959
   104     3     7       0.125       0.375        0.481923        0.478553      0.00336996
   105     4     7      0.1875       0.375        0.705116         0.70078      0.00433565
   106     5     7        0.25       0.375        0.908359        0.903281       0.0050778
   107     6     7      0.3125       0.375         1.08631         1.08068      0.00563042
   108     7     7       0.375       0.375         1.23452         1.22855      0.00596777
   109     8     7      0.4375       0.375          1.3497         1.34363      0.00607475
   110     9     7         0.5       0.375         1.42983         1.42388      0.00594887
   111    10     7      0.5625       0.375         1.47422         1.46863      0.00559372
   112    11     7       0.625       0.375         1.48358         1.47855      0.00502533
   113    12     7      0.6875       0.375         1.45994         1.45568      0.00425823
   114    13     7        0.75       0.375         1.40663         1.40328      0.00334663
   115    14     7      0.8125       0.375         1.32802         1.32578      0.00224019
   116    15     7       0.875       0.375         1.22982         1.22855      0.00126534
   117    16     7      0.9375       0.375         1.11728         1.11774     0.000456313
   118    17     7           1       0.375               1               1               0

   119     1     8           0      0.4375               0               0               0
   120     2     8      0.0625      0.4375        0.255775        0.253842      0.00193347
   121     3     8       0.125      0.4375        0.503328         0.50033      0.00299745
   122     4     8      0.1875      0.4375         0.73642        0.732395      0.00402493
   123     5     8        0.25      0.4375        0.948433         0.94352      0.00491285
   124     6     8      0.3125      0.4375         1.13359         1.12799      0.00559825
   125     7     8       0.375      0.4375          1.2872         1.28113      0.00607475
   126     8     8      0.4375      0.4375         1.40576         1.39944      0.00631544
   127     9     8         0.5      0.4375          1.4871         1.48079      0.00631436
   128    10     8      0.5625      0.4375         1.53051         1.52444      0.00606995
   129    11     8       0.625      0.4375         1.53672         1.53113      0.00559372
   130    12     8      0.6875      0.4375         1.50789         1.50299      0.00489781
   131    13     8        0.75      0.4375         1.44755         1.44352      0.00402943
   132    14     8      0.8125      0.4375         1.36035          1.3574      0.00295607
   133    15     8       0.875      0.4375         1.25225         1.25033      0.00192411
   134    16     8      0.9375      0.4375         1.12921         1.12884     0.000364567
   135    17     8           1      0.4375               1               1               0

   136     1     9           0         0.5               0               0               0
   137     2     9      0.0625         0.5        0.258762         0.25759      0.00117132
   138     3     9       0.125         0.5        0.510192        0.507683      0.00250889
   139     4     9      0.1875         0.5        0.746629         0.74307      0.00355884
   140     5     9        0.25         0.5        0.961666        0.957107      0.00455886
   141     6     9      0.3125         0.5         1.14932         1.14397      0.00535113
   142     7     9       0.375         0.5         1.30483         1.29888      0.00594887
   143     8     9      0.4375         0.5          1.4246         1.41829      0.00631436
   144     9     9         0.5         0.5         1.50644             1.5       0.0064384
   145    10     9      0.5625         0.5          1.5496         1.54329      0.00631436
   146    11     9       0.625         0.5         1.55483         1.54888      0.00594887
   147    12     9      0.6875         0.5         1.52432         1.51897      0.00535113
   148    13     9        0.75         0.5         1.46167         1.45711      0.00455886
   149    14     9      0.8125         0.5         1.37163         1.36807      0.00355884
   150    15     9       0.875         0.5         1.26019         1.25768      0.00250889
   151    16     9      0.9375         0.5         1.13376         1.13259      0.00117132
   152    17     9           1         0.5               1               1               0

   153     1    10           0      0.5625               0               0               0
   154     2    10      0.0625      0.5625        0.254206        0.253842     0.000364567
   155     3    10       0.125      0.5625        0.502254         0.50033      0.00192411
   156     4    10      0.1875      0.5625        0.735351        0.732395      0.00295607
   157     5    10        0.25      0.5625        0.947549         0.94352      0.00402943
   158     6    10      0.3125      0.5625         1.13289         1.12799      0.00489781
   159     7    10       0.375      0.5625         1.28672         1.28113      0.00559372
   160     8    10      0.4375      0.5625         1.40551         1.39944      0.00606995
   161     9    10         0.5      0.5625          1.4871         1.48079      0.00631436
   162    10    10      0.5625      0.5625         1.53076         1.52444      0.00631544
   163    11    10       0.625      0.5625          1.5372         1.53113      0.00607475
   164    12    10      0.6875      0.5625         1.50859         1.50299      0.00559825
   165    13    10        0.75      0.5625         1.44843         1.44352      0.00491285
   166    14    10      0.8125      0.5625         1.36142          1.3574      0.00402493
   167    15    10       0.875      0.5625         1.25333         1.25033      0.00299745
   168    16    10      0.9375      0.5625         1.13078         1.12884      0.00193347
   169    17    10           1      0.5625               1               1               0

   170     1    11           0       0.625               0               0               0
   171     2    11      0.0625       0.625        0.242284         0.24274     0.000456313
   172     3    11       0.125       0.625        0.479819        0.478553      0.00126534
   173     4    11      0.1875       0.625         0.70302         0.70078      0.00224019
   174     5    11        0.25       0.625        0.906628        0.903281      0.00334663
   175     6    11      0.3125       0.625         1.08494         1.08068      0.00425823
   176     7    11       0.375       0.625         1.23358         1.22855      0.00502533
   177     8    11      0.4375       0.625         1.34922         1.34363      0.00559372
   178     9    11         0.5       0.625         1.42983         1.42388      0.00594887
   179    10    11      0.5625       0.625          1.4747         1.46863      0.00607475
   180    11    11       0.625       0.625         1.48452         1.47855      0.00596777
   181    12    11      0.6875       0.625         1.46131         1.45568      0.00563042
   182    13    11        0.75       0.625         1.40836         1.40328       0.0050778
   183    14    11      0.8125       0.625         1.33012         1.32578      0.00433565
   184    15    11       0.875       0.625         1.23192         1.22855      0.00336996
   185    16    11      0.9375       0.625         1.12036         1.11774      0.00261959
   186    17    11           1       0.625               1               1               0

   187     1    12           0      0.6875               0               0               0
   188     2    12      0.0625      0.6875        0.223452        0.224712       0.0012595
   189     3    12       0.125      0.6875        0.443747         0.44319     0.000557444
   190     4    12      0.1875      0.6875        0.650874         0.64944      0.00143454
   191     5    12        0.25      0.6875        0.840466        0.837938      0.00252838
   192     6    12      0.3125      0.6875         1.00729         1.00384      0.00344814
   193     7    12       0.375      0.6875         1.14744         1.14318      0.00425823
   194     8    12      0.4375      0.6875         1.25789         1.25299      0.00489781
   195     9    12         0.5      0.6875         1.33682         1.33147      0.00535113
   196    10    12      0.5625      0.6875         1.38359         1.37799      0.00559825
   197    11    12       0.625      0.6875         1.39881         1.39318      0.00563042
   198    12    12      0.6875      0.6875         1.38429         1.37884      0.00544661
   199    13    12        0.75      0.6875         1.34299         1.33794      0.00504935
   200    14    12      0.8125      0.6875         1.27892         1.27444      0.00448298
   201    15    12       0.875      0.6875         1.19681         1.19319      0.00361675
   202    16    12      0.9375      0.6875         1.10292         1.09971      0.00321207
   203    17    12           1      0.6875               1               1               0

   204     1    13           0        0.75               0               0               0
   205     2    13      0.0625        0.75        0.198435         0.20045      0.00201456
   206     3    13       0.125        0.75        0.395433        0.395598      0.00016549
   207     4    13      0.1875        0.75        0.580942        0.580347      0.00059487
   208     5    13        0.25        0.75         0.75164            0.75      0.00164007
   209     6    13      0.3125        0.75        0.902966        0.900438      0.00252838
   210     7    13       0.375        0.75         1.03163         1.02828      0.00334663
   211     8    13      0.4375        0.75         1.13505         1.13102      0.00402943
   212     9    13         0.5        0.75         1.21167         1.20711      0.00455886
   213    10    13      0.5625        0.75         1.26093         1.25602      0.00491285
   214    11    13       0.625        0.75         1.28336         1.27828       0.0050778
   215    12    13      0.6875        0.75         1.28049         1.27544      0.00504935
   216    13    13        0.75        0.75         1.25482            1.25      0.00481787
   217    14    13      0.8125        0.75         1.20979         1.20535      0.00444373
   218    15    13       0.875        0.75         1.14931          1.1456      0.00370845
   219    16    13      0.9375        0.75          1.0791         1.07545      0.00365301
   220    17    13           1        0.75               1               1               0

   221     1    14           0      0.8125               0               0               0
   222     2    14      0.0625      0.8125         0.16819        0.170886      0.00269655
   223     3    14       0.125      0.8125        0.336675        0.337608     0.000932687
   224     4    14      0.1875      0.8125        0.495792        0.496158     0.000366704
   225     5    14        0.25      0.8125        0.643442        0.642847      0.00059487
   226     6    14      0.3125      0.8125        0.775874         0.77444      0.00143454
   227     7    14       0.375      0.8125         0.89052         0.88828      0.00224019
   228     8    14      0.4375      0.8125        0.985351        0.982395      0.00295607
   229     9    14         0.5      0.8125         1.05913         1.05557      0.00355884
   230    10    14      0.5625      0.8125         1.11142          1.1074      0.00402493
   231    11    14       0.625      0.8125         1.14262         1.13828      0.00433565
   232    12    14      0.6875      0.8125         1.15392         1.14944      0.00448298
   233    13    14        0.75      0.8125         1.14729         1.14285      0.00444373
   234    14    14      0.8125      0.8125         1.12545         1.12116      0.00429513
   235    15    14       0.875      0.8125         1.09133         1.08761       0.0037244
   236    16    14      0.9375      0.8125         1.04995         1.04589      0.00406452
   237    17    14           1      0.8125               1               1               0

   238     1    15           0       0.875               0               0               0
   239     2    15      0.0625       0.875        0.133953        0.137158      0.00320434
   240     3    15       0.125       0.875        0.270092        0.271447        0.001355
   241     4    15      0.1875       0.875        0.399175        0.400108     0.000932687
   242     5    15        0.25       0.875        0.520433        0.520598      0.00016549
   243     6    15      0.3125       0.875        0.631247         0.63069     0.000557444
   244     7    15       0.375       0.875        0.729819        0.728553      0.00126534
   245     8    15      0.4375       0.875        0.814754         0.81283      0.00192411
   246     9    15         0.5       0.875        0.885192        0.882683      0.00250889
   247    10    15      0.5625       0.875        0.940828         0.93783      0.00299745
   248    11    15       0.625       0.875        0.981923        0.978553      0.00336996
   249    12    15      0.6875       0.875         1.00931         1.00569      0.00361675
   250    13    15        0.75       0.875         1.02431          1.0206      0.00370845
   251    14    15      0.8125       0.875         1.02883         1.02511       0.0037244
   252    15    15       0.875       0.875         1.02477         1.02145      0.00332555
   253    16    15      0.9375       0.875         1.01604         1.01216      0.00388708
   254    17    15           1       0.875               1               1               0

   255     1    16           0      0.9375               0               0               0
   256     2    16      0.0625      0.9375       0.0962937         0.10056      0.00426653
   257     3    16       0.125      0.9375        0.196453        0.199658      0.00320434
   258     4    16      0.1875      0.9375         0.29319        0.295886      0.00269655
   259     5    16        0.25      0.9375        0.385935         0.38795      0.00201456
   260     6    16      0.3125      0.9375        0.473452        0.474712       0.0012595
   261     7    16       0.375      0.9375        0.554784         0.55524     0.000456313
   262     8    16      0.4375      0.9375        0.629206        0.628842     0.000364567
   263     9    16         0.5      0.9375        0.696262         0.69509      0.00117132
   264    10    16      0.5625      0.9375        0.755775        0.753842      0.00193347
   265    11    16       0.625      0.9375         0.80786         0.80524      0.00261959
   266    12    16      0.6875      0.9375        0.852924        0.849712      0.00321207
   267    13    16        0.75      0.9375        0.891603         0.88795      0.00365301
   268    14    16      0.8125      0.9375        0.924951        0.920886      0.00406452
   269    15    16       0.875      0.9375        0.953545        0.949658      0.00388708
   270    16    16      0.9375      0.9375         0.98079         0.97556      0.00522933
   271    17    16           1      0.9375               1               1               0

   272     1    17           0           1               0               0               0
   273     2    17      0.0625           1          0.0625          0.0625               0
   274     3    17       0.125           1           0.125           0.125               0
   275     4    17      0.1875           1          0.1875          0.1875               0
   276     5    17        0.25           1            0.25            0.25               0
   277     6    17      0.3125           1          0.3125          0.3125               0
   278     7    17       0.375           1           0.375           0.375               0
   279     8    17      0.4375           1          0.4375          0.4375               0
   280     9    17         0.5           1             0.5             0.5               0
   281    10    17      0.5625           1          0.5625          0.5625               0
   282    11    17       0.625           1           0.625           0.625               0
   283    12    17      0.6875           1          0.6875          0.6875               0
   284    13    17        0.75           1            0.75            0.75               0
   285    14    17      0.8125           1          0.8125          0.8125               0
   286    15    17       0.875           1           0.875           0.875               0
   287    16    17      0.9375           1          0.9375          0.9375               0
   288    17    17           1           1               1               1               0


  ||U||   = 0.996235
  ||W||   = 0.994293
  ||U-W|| = 0.0623472

FEM2D_LEASTSQUARES:
  Normal end of execution.