fem1d


fem1d, a C code which applies the finite element method (FEM) to a linear two point boundary value problem in one spatial dimension.

Licensing:

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

Languages:

fem1d is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

FEM1D, a data directory which contains examples of 1D FEM files, three text files that describe a 1D finite element model;

fem1d_test

FEM1D_ADAPTIVE, a C code which applies the finite element method to a linear two point boundary value problem in a 1D region, using adaptive refinement to improve the solution.

FEM1D_BVP_LINEAR, a C code which applies the finite element method, with piecewise linear elements, to a two point boundary value problem in one spatial dimension.

FEM1D_LAGRANGE, a C code which sets up the matrices and vectors associated with the finite element method (FEM) solution of a boundary value problem (BVP) -u''+u=f(x), using Lagrange basis polynomials.

FEM1D_NONLINEAR, a C code which applies the finite element method to a nonlinear two point boundary value problem in a 1D region.

FEM1D_PMETHOD, a C code which applies the p-method version of the finite element method to a linear two point boundary value problem in a 1D region.

FEM1D_PROJECT, a C code which projects data into a finite element space, including the least squares approximation of data, or the projection of a finite element solution from one mesh to another.

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

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.

Reference:

  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:


Last revised on 21 June 2019.