Evaluate a Finite Element Function of a 2D Argument

FEM2D_SAMPLE is a C++ program which can evaluate a finite element function of a 2D argument.

The current version of the program can only handle finite element meshes which are made of piecewise linear triangles of order 3 or 6.


fem2d_sample fem_prefix sample_prefix
where fem_prefix is the common prefix for the FEM files: and sample_prefix is the common prefix for the SAMPLE files, for which the node file is input, and the values file is created by the program:


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


FEM2D_SAMPLE is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

FEM1D_SAMPLE, a C++ program which samples a scalar or vector finite element function of one variable, defined by FEM files, returning interpolated values at the sample points.

FEM2D, a data directory which contains examples of 2D FEM files, three text files that describe a 2D finite element geometry;

FEM2D_HEAT, a C++ program which solves the time dependent heat equation in the unit square.

FEM2D_PACK, a C++ library which includes utitlies for 2D finite element calculations.

FEM2D_POISSON, a C++ program which solves Poisson's equation on a square, using the finite element method.

FEM2D_POISSON_LINEAR, a C++ program which solves the 2D Poisson equation on a rectangle, using the finite element method, and piecewise linear triangular elements.

FEM2D_PROJECT, a C++ program which projects a function F(X,Y) into a given finite element space of piecewise linear triangular elements.

FEM3D_SAMPLE, a C++ program which evaluates a finite element function defined on 3D tetrahedral mesh.

HISTOGRAM_DATA_2D_SAMPLE, a C++ program which demonstrates how to construct a Probability Density Function (PDF) from a frequency table over a 2D domain, and then to use that PDF to create new samples.


  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:

Examples and Tests:

SQ is FEM data for the function f(x,y)=x^2+y^2, on a 5x5 grid of nodes, organized into linear triangles. The sample data seeks the values of this function on a 4x4 evenly spaced grid.

List of Routines:

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

Last revised on 08 August 2009.