fem2d_heat_rectangle_test

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.

Licensing:

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

Related Data and codes:

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.

Source Code:

• 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;