**fem2d_heat_test**,
a MATLAB program which
calls fem2d_heat() to
solve a 2D heat equation posed in the unit square,
using the finite element method (FEM).

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

fem2d_heat, a MATLAB program which uses the finite element method and the backward Euler method to solve the 2D time-dependent heat equation on an arbitrary triangulated region. In order to run, it requires user-supplied routines that define problem data.

- fem2d_heat_test.m, calls all the tests.
- fem2d_heat_test.sh, runs all the tests.
- fem2d_heat_test.txt, the output file.

- dirichlet_condition.m, the user-supplied routine to evaluate the boundary conditions;
- initial_condition.m, the user-supplied routines to evaluate the initial conditions;
- k_coef.m, the user-supplied routines to evaluate the linear coefficient.
- rhs.m, the user-supplied routines to evaluate the right hand side;
- square.txt, output from a run of the program;
- square_nodes.png, a PNG image of the 49 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 32 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;