**fem2d_heat_rectangle_test**,
a FORTRAN90 code which
calls fem2d_heat_rectangle(), which
solves the time-dependent 2D heat equation
using the finite element method in space, and a method of
lines in time with the backward Euler approximation for the
time derivative, over a rectangular region with a uniform grid.

The computer code and data files described and made available on this web page are distributed under the MIT license

fem2d_heat_rectangle, a FORTRAN90 code which uses the finite element method (FEM) to solve the 2D time dependent heat equation on the unit square, using a uniform grid of triangular elements.

- fem2d_heat_rectangle_test.sh, runs all the tests.
- fem2d_heat_rectangle_test.txt, the output file.

- nodes.png, a PNG image of the 49 nodes;
- nodes.txt, a text file containing a list, for each node, of its X and Y coordinates;
- elements.png, a PNG image of the 32 elements;
- elements.txt, a text file containing a list, for each element, of the six nodes that compose it;
- 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 code **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;