10 September 2006 07:50:01 AM

FREE_FEM_HEAT (C++ version):
  Solution of the time dependent heat equation
  on an arbitrary triangulated region D in 2 dimensions.

  Ut - Uxx - Uyy + K(x,y,t) * U = F(x,y,t) in D
                              U = G(x,y,t) on the 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 method.

  Current status:

  * The time step information must be set internally.
  * Would be easy to do linear triangles as well.
  * Do you want ability to compare 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             0
    2          0.125             0
    3           0.25             0
    4          0.375             0
    5            0.5             0
    6          0.625             0
    7           0.75             0
    8          0.875             0
    9              1             0
   10              0         0.125


  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
  Final time =   0.5
  Step size =    0.05
  Number of steps = 10
  Wrote solution file "u0000.txt" for time T = 0

Time  L2 Error H1 Error

  Wrote solution file "u0001.txt" for time T = 0.05
  Wrote solution file "u0002.txt" for time T = 0.1
  Wrote solution file "u0003.txt" for time T = 0.15
  Wrote solution file "u0004.txt" for time T = 0.2
  Wrote solution file "u0005.txt" for time T = 0.25
  Wrote solution file "u0006.txt" for time T = 0.3
  Wrote solution file "u0007.txt" for time T = 0.35
  Wrote solution file "u0008.txt" for time T = 0.4
  Wrote solution file "u0009.txt" for time T = 0.45
  Wrote solution file "u0010.txt" for time T = 0.5

FREE_FEM_HEAT:
  Normal end of execution.

10 September 2006 07:50:01 AM