A Problem in a Square Region for FEM2D_HEAT

FEM2D_HEAT_SQUARE is a MATLAB library which defines the geometry and other data for the the heat equation over a square region, for solution by FEM2D_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).
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 MATLAB version.

Related Data and Programs:

CONTOUR_SEQUENCE4, a MATLAB program which makes a sequence of contour plots based on a single XY coordinate file, and a sequence of Z(X,Y) data files.

FEM2D_HEAT, a MATLAB program which uses the finite element method and the backward Euler method to solve the 2D time-dependent heat equation on an arbitrary triangulated region. In order to run, it requires user-supplied routines that define problem data.

TRIANGULATION_DISPLAY, a MATLAB program which displays the nodes and elements of a triangulation on the MATLAB graphics screen;


  1. Hans Rudolf Schwarz,
    Finite Element Methods,
    Academic Press, 1988,
    ISBN: 0126330107,
    LC: TA347.F5.S3313.
  2. Gilbert Strang, George Fix,
    An Analysis of the Finite Element Method,
    Cambridge, 1973,
    ISBN: 096140888X,
    LC: TA335.S77.
  3. Olgierd Zienkiewicz,
    The Finite Element Method,
    Sixth Edition,
    Butterworth-Heinemann, 2005,
    ISBN: 0750663200,
    LC: TA640.2.Z54

Source Code:

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

You can go up one level to the MATLAB source code page.

Last revised on 11 January 2011.