fem2d_heat_test
fem2d_heat_test,
a C++ code which
calls fem2d_heat(), which
applies the finite element method to solve
a form of the time-dependent heat equation over an arbitrary
triangulated region.
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*pi-1)*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 MIT license
Related Programs:
fem2d_heat,
a C++ code which
applies the finite element method to solve
a form of the time-dependent heat equation over an arbitrary
triangulated region.
Source Code:
-
square_nodes.txt,
a text file containing a list, for each node, of its X and Y
coordinates;
-
square_elements.txt,
a text file containing a list, for each element, of the six
nodes that compose it;
-
square_nodes.png,
a PNG image of
the nodes;
-
square_elements.png,
a PNG image of
the elements;
-
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;
Last revised on 05 March 2020.