A Problem in a Square Region for FEM2D_HEAT_

FEM2D_HEAT_SQUARE is a C++ library which defines the data associated with a time-dependent heat equation problem in a square region, to be linked and executed with the FEM2D_HEAT program.

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).
The exact solution is:
U = sin(pi*x) * sin(pi*y) * exp(-t).
which is the formula we use to define our functions G (for the boundary conditions) and H (for the initial conditions).


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


FEM2D_HEAT_SQUARE is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Source Code:

The MATLAB program CONTOUR_SEQUENCE4 can make contour plots from the sequence of solutions:

You can go up one level to the C++ source codes.

Last revised on 30 August 2006.