fem1d_heat_implicit_test

fem1d_heat_implicit_test, an Octave code which calls fem1d_heat_implicit(), which solves the time-dependent 1D heat equation, using the finite element method in space, and an implicit version of the method of lines, using the backward Euler method, to handle integration in time.

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:

fem1d_heat_implicit, an Octave code which uses the finite element method (FEM) and implicit time stepping to solve the time dependent heat equation in 1D.

Source Code:

• fem1d_heat_implicit_test.m, calls all the tests.
• fem1d_heat_implicit_test.sh, runs all the tests.
• fem1d_heat_implicit_test.txt, the output file.

• fem1d_heat_implicit_test01.m, runs test 1;
• fem1d_heat_implicit_test02.m, runs test 2;
• fem1d_heat_implicit_test03.m, runs test 3;

TEST01 runs with initial condition 50 everywhere, boundary conditions of 90 on the left and 70 on the right, and no right hand side source term.

• bc_test01.m, enforces the boundary conditions.
• h_test01.txt, the computed H data.
• ic_test01.m, enforces the initial condition.
• k_test01.m, sets the conductivity.
• plot_test01.png, a PNG image of the solution.
• rhs_test01.m, supplies the right hand side source term.
• t_test01.txt, the T data.
• x_test01.txt, the X data.

TEST02 uses an exact solution of g(x,t) = exp ( - t ) .* sin ( sqrt ( k ) * x ).

• bc_test02.m, enforces the boundary conditions.
• exact_test02.m, evaluates the exact solution.
• g_test02.txt, the exact data.
• h_test02.txt, the computed H data.
• ic_test02.m, enforces the initial condition.
• k_test02.m, sets the conductivity.
• plot_test02.png, a PNG image of the solution.
• plot_g_test02.png, a PNG image of the exact solution.
• rhs_test02.m, supplies the right hand side source term.
• t_test02.txt, the T data.
• x_test02.txt, the X data.

TEST03 runs on the interval -5 <= X <= 5, with initial condition 15 on the entire left and 25 on the entire right. The solution should settle down to a straight line from the left boundary to the right.

• bc_test03.m, enforces the boundary conditions.
• h_test03.txt, the computed H data.
• ic_test03.m, enforces the initial condition.
• k_test03.m, sets the conductivity.
• plot_test03.png, a PNG image of the solution.
• rhs_test03.m, supplies the right hand side source term.
• t_test03.txt, the T data.
• x_test03.txt, the X data.