fem2d_heat_rectangle_test

fem2d_heat_rectangle_test, a C++ 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.

Licensing:

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

Related Data and Programs:

fem2d_heat_rectangle, a C++ 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.

• fem2d_heat_rectangle_nodes.png, a PNG image of the nodes, for NX = NY = 7 (the picture is hard to read for larger values of NX and NY);
• rectangle_nodes.txt, a text file containing a list, for each node, of its X and Y coordinates;
• rectangle_elements.png, a PNG image of the elements, for NX = NY = 7 (the picture is hard to read for larger values of NX and NY);
• rectangle_elements.txt, a text file containing a list, for each element, of the six nodes that compose it;
• rectangle_time.txt, a text file containing the solution times;
• rectangle_u0000.txt, the solution U at time step 0;
• rectangle_u0001.txt, the solution U at time step 1;
• rectangle_u0002.txt, the solution U at time step 2;
• rectangle_u0003.txt, the solution U at time step 3;
• rectangle_u0004.txt, the solution U at time step 4;
• rectangle_u0005.txt, the solution U at time step 5;
• rectangle_u0006.txt, the solution U at time step 6;
• rectangle_u0007.txt, the solution U at time step 7;
• rectangle_u0008.txt, the solution U at time step 8;
• rectangle_u0009.txt, the solution U at time step 9;
• rectangle_u0010.txt, the solution U at time step 10;

The MATLAB program CONTOUR_SEQUENCE4 can make contour plots from the sequence of solutions:

• rectangle_u0000.png, the solution U at time step 0;
• rectangle_u0001.png, the solution U at time step 1;
• rectangle_u0002.png, the solution U at time step 2;
• rectangle_u0003.png, the solution U at time step 3;
• rectangle_u0004.png, the solution U at time step 4;
• rectangle_u0005.png, the solution U at time step 5;
• rectangle_u0006.png, the solution U at time step 6;
• rectangle_u0007.png, the solution U at time step 7;
• rectangle_u0008.png, the solution U at time step 8;
• rectangle_u0009.png, the solution U at time step 9;
• rectangle_u0010.png, the solution U at time step 10;