free_fem_heat ( 'square_nodes.txt', 'square_elements.txt' )
29-Aug-2006 08:37:12

FREE_FEM_HEAT (MATLAB version):
  Solution of the time dependent heat equation
  on an arbitrary triangulated region D in 2 dimensions.n
  Ut - Uxx - Uyy + K(x,y,t) * U = F(x,y,t) in D;
                              U = G(x,y,t) on boundary;
                              U = H(x,y,t) at initial time.

  The finite element method is used, with
  6 node quadratic triangular elements ("T6").

  The time derivative is approximated using the
  backward Euler formula.

  Current status:

  * Time step information currently set internally!
  * Would be easy to do linear triangles as well.
  * Do you want ability to compare to an exact solution?


  Node file is "square_nodes.txt".
  Element file is "square_elements.txt".
  Number of nodes =          81

  First 10 nodes

  Row:       1             2       
  Col
    1     0.000000    0.000000
    2     0.125000    0.000000
    3     0.250000    0.000000
    4     0.375000    0.000000
    5     0.500000    0.000000
    6     0.625000    0.000000
    7     0.750000    0.000000
    8     0.875000    0.000000
    9     1.000000    0.000000
   10     0.000000    0.125000

  Element order =            6
  Number of elements =       32

  First 10 elements

  Row:       1        2        3        4        5        6  
  Col

    1        1       19        3       10       11        2  
    2       21        3       19       12       11       20  
    3        3       21        5       12       13        4  
    4       23        5       21       14       13       22  
    5        5       23        7       14       15        6  
    6       25        7       23       16       15       24  
    7        7       25        9       16       17        8  
    8       27        9       25       18       17       26  
    9       19       37       21       28       29       20  
   10       39       21       37       30       29       38  


  Quadrature order =          3

  The matrix half bandwidth is 18
  The matrix bandwidth is      37
  The storage bandwidth is     55

  Initial time = 0.000000
  Final time =   0.500000
  Step size =    0.050000
  Number of steps = 10
  Wrote the solution file "u0000.txt" for time T = 0.000000.

Time  L2 Error H1 Error

  Wrote the solution file "u0001.txt" for time T = 0.050000.
  Wrote the solution file "u0002.txt" for time T = 0.100000.
  Wrote the solution file "u0003.txt" for time T = 0.150000.
  Wrote the solution file "u0004.txt" for time T = 0.200000.
  Wrote the solution file "u0005.txt" for time T = 0.250000.
  Wrote the solution file "u0006.txt" for time T = 0.300000.
  Wrote the solution file "u0007.txt" for time T = 0.350000.
  Wrote the solution file "u0008.txt" for time T = 0.400000.
  Wrote the solution file "u0009.txt" for time T = 0.450000.
  Wrote the solution file "u0010.txt" for time T = 0.500000.

FREE_FEM_HEAT:
  Normal end of execution.

29-Aug-2006 08:37:21
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