fem1d_spectral_numeric

fem1d_spectral_numeric, a MATLAB code which applies the spectral finite element method to solve the problem u'' = - pi^2 sin(x) over [-1,+1] with zero boundary conditions, using as basis elements the functions x^n*(x-1)*(x+1), and carrying out the integration numerically using MATLAB's quad() function, by Miro Stoyanov.

This function solves the problem u'' = - pi^2 * sin( pi * x ) for x in (-1,1), with boundary conditions u(-1) = u(1) = 0.

This problem has exact solution u(x) = sin(pi*x).

We use the spectral finite element method. We assume that the solution can be written in terms of polynomials:

```        phi_1 = x^0     * (x-1)*(x+1),
phi_2 = x^1     * (x-1)*(x+1)
...
phi_i = x^(i-1) * (x-1)*(x+1) ...
```
For this particular problem, the solution is an odd function, so only every other basis function will actually be useful.

Licensing:

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

Languages:

fem1d_spectral_numeric is available in a MATLAB version.

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Author:

Miroslav Stoyanov, Oak Ridge National Laboratory.

Reference:

1. Gilbert Strang, George Fix,
An Analysis of the Finite Element Method,
Cambridge, 1973,
ISBN: 096140888X,
LC: TA335.S77.

Source Code:

Last revised on 20 January 2019.