Finite Element Routines

FEM2D_PACK is a C library which implements the finite element method.

The emphasis is on simplicity and clarity. Only the 2D case is handled, with a choice of low order triangular and quadrilateral elements.

A few routines are included for computing a "sphere grid", that is, a finite element mesh on the surface of a sphere.


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


FEM2D_PACK is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

FEM_BASIS, a C library which can define basis functions for the finite element method (FEM) for any degree in an M-dimensional simplex (1D interval, 2D triangle, 3D tetrahedron, and higher dimensional generalizations.)

FEM1D_PACK, a C++ library which contains utilities for 1D finite element calculations.

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 on the unit square.

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

FEM2D_POISSON_RECTANGLE_LINEAR, a C++ program which solves the 2D Poisson equation on a rectangle, using the finite element method, and piecewise linear triangular elements.

FEM2D_SAMPLE, a C++ library which evaluates a finite element function defined on an order 3 or order 6 triangulation.


  1. Milton Abramowitz, Irene Stegun,
    Handbook of Mathematical Functions,
    National Bureau of Standards, 1964,
    ISBN: 0-486-61272-4,
    LC: QA47.A34.
  2. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
    LINPACK User's Guide,
    SIAM, 1979,
    ISBN13: 978-0-898711-72-1.
  3. Vladimir Krylov,
    Approximate Calculation of Integrals,
    Dover, 2006,
    ISBN: 0486445798.
  4. Hans Rudolf Schwarz,
    Finite Element Methods,
    Academic Press, 1988,
    ISBN: 0126330107,
    LC: TA347.F5.S3313..
  5. Gilbert Strang, George Fix,
    An Analysis of the Finite Element Method,
    Cambridge, 1973,
    ISBN: 096140888X,
    LC: TA335.S77.
  6. Arthur Stroud,
    Approximate Calculation of Multiple Integrals,
    Prentice Hall, 1971,
    ISBN: 0130438936,
    LC: QA311.S85.
  7. Arthur Stroud, Don Secrest,
    Gaussian Quadrature Formulas,
    Prentice Hall, 1966,
    LC: QA299.4G3S7.
  8. Olgierd Zienkiewicz,
    The Finite Element Method,
    Sixth Edition,
    Butterworth-Heinemann, 2005,
    ISBN: 0750663200.
  9. Daniel Zwillinger, editor,
    CRC Standard Mathematical Tables and Formulae,
    30th Edition,
    CRC Press, 1996,
    ISBN: 0-8493-2479-3.

Source Code:

Examples and Tests:

List of Routines:

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

Last revised on 16 January 2013.