fem2d_heat_test

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).

Licensing:

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

Related Data and Programs:

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.

Source Code:

• 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;