SQUARE
A Problem in a Square Region for FREE_FEM_HEAT

The SQUARE problem uses the geometry of a square region. This is an example of how to specify a problem to be solved by FREE_FEM_HEAT.

This mesh uses 81 nodes and forms 32 quadratic triangular elements.

We assume that the equation to be solved is

dUdT - Laplacian U + K * U = F

K = 0,

F = (2*pi*pi-1)*sin(pi*x)*sin(pi*y)*exp(-t).

U = sin(pi*x) * sin(pi*y) * exp(-t).

• square.f90, the user-supplied routines to evaluate the right hand side, linear coefficient, initial and boundary conditions;
• square.csh, commands to compile the user routines, link them with the partial program, and run the program;
• square_output.txt, the output file.
• 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;

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