**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

withdUdT - Laplacian U + K * U = F

andK = 0,

The exact solution is:F = (2*pi*pi-1)*sin(pi*x)*sin(pi*y)*exp(-t).

which is the formula we use to define our functionsU = sin(pi*x) * sin(pi*y) * exp(-t).

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

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.

- fem2d_heat_test.cpp, the user-supplied routines to evaluate the right hand side, linear coefficient, initial and boundary conditions;
- fem2d_heat_test.sh, runs all the tests.
- fem2d_heat_test.txt, the output file.

- 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;