fem1d_heat_explicit_test

fem1d_heat_explicit_test, a MATLAB code which calls fem1d_heat_explicit(), which solves the time-dependent 1D heat equation, using the finite element method in space, and an explicit version of the method of lines 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_explicit, a MATLAB code which uses the finite element method (FEM) and explicit time stepping to solve the time dependent heat equation in 1D.

Source Code:

• fem1d_heat_explicit_test.m, calls all the tests.
• fem1d_heat_explicit_test.sh, runs all the tests.
• fem1d_heat_explicit_test.txt, the output file.

• fem1d_heat_explicit_test01.m, runs test 1;
• fem1d_heat_explicit_test02.m, runs test 2;
• fem1d_heat_explicit_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.
• 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.