FEM2D_HEAT_SQUARE
A Problem in a Square Region for FEM2D_HEAT_
FEM2D_HEAT_SQUARE is a C++ library which
defines the data associated with a timedependent heat equation
problem in a square region, to be linked and executed with the
FEM2D_HEAT program.
This mesh uses 81 nodes and forms 32 quadratic triangular elements.
We assume that the equation to be solved is
dUdT  Laplacian U + K * U = F
with
K = 0,
and
F = (2*pi*pi1)*sin(pi*x)*sin(pi*y)*exp(t).
The exact solution is:
U = sin(pi*x) * sin(pi*y) * exp(t).
which is the formula we use to define our functions G
(for the boundary conditions) and H (for the initial
conditions).
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
FEM2D_HEAT_SQUARE is available in
a C++ version and
a FORTRAN90 version and
a MATLAB version.
Source Code:

square.cpp,
the usersupplied routines to evaluate the right hand side,
linear coefficient, initial and boundary conditions;

square_output.txt,
output from a run of the program;

square_nodes.png,
a PNG image of
the nodes;

square_nodes.txt,
a text file containing a list, for each node, of its X and Y
coordinates;

square_elements.png,
a PNG image of
the elements;

square_elements.txt,
a text file containing a list, for each element, of the six
nodes that compose it;

square_time.txt,
a text file containing the solution times;

u0000.txt,
the solution U at time step 0;

u0001.txt,
the solution U at time step 1;

u0002.txt,
the solution U at time step 2;

u0003.txt,
the solution U at time step 3;

u0004.txt,
the solution U at time step 4;

u0005.txt,
the solution U at time step 5;

u0006.txt,
the solution U at time step 6;

u0007.txt,
the solution U at time step 7;

u0008.txt,
the solution U at time step 8;

u0009.txt,
the solution U at time step 9;

u0010.txt,
the solution U at time step 10;
The MATLAB program CONTOUR_SEQUENCE4 can make contour
plots from the sequence of solutions:

u0000.png,
the solution U at time step 0;

u0001.png,
the solution U at time step 1;

u0002.png,
the solution U at time step 2;

u0003.png,
the solution U at time step 3;

u0004.png,
the solution U at time step 4;

u0005.png,
the solution U at time step 5;

u0006.png,
the solution U at time step 6;

u0007.png,
the solution U at time step 7;

u0008.png,
the solution U at time step 8;

u0009.png,
the solution U at time step 9;

u0010.png,
the solution U at time step 10;
You can go up one level to
the C++ source codes.
Last revised on 30 August 2006.