FEM1D
Piecewise Linear Finite Element Method for 1D problem.

FEM1D is a C++ program which applies the finite element method (FEM) to a linear two point boundary value problem (BVP) in one spatial dimension.

Licensing:

The computer code described and made available on this web page are distributed under the GNU LGPL 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_ADAPTIVE, a C++ program 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++ program which applies the finite element method, with piecewise linear elements, to a two point boundary value problem in one spatial dimension.

FEM1D_HEAT_STEADY, a C++ program which uses the finite element method to solve the steady (time independent) heat equation in 1D.

FEM1D_LAGRANGE, a C++ library 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++ program which applies the finite element method to a nonlinear two point boundary value problem in a 1D region.

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

FEM1D_PMETHOD, a C++ program 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++ program 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++ program which samples a scalar or vector finite element function of one variable, defined by FEM files, returning interpolated values at the sample points.

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:

• fem1d.cpp, the source code.

Examples and Tests:

• fem1d_output.txt, the output file.

List of Routines:

• MAIN is the main program for FEM1D.
• ASSEMBLE assembles the matrix and right-hand-side of the linear system.
• FF evaluates the right hand side function.
• GEOMETRY sets up the geometry for the interval [XL,XR].
• INIT assigns values to variables which define the problem.
• OUTPUT prints out the computed solution.
• PHI evaluates a linear basis function and its derivative.
• PP evaluates the function P in the differential equation.
• PRSYS prints out the tridiagonal linear system.
• QQ evaluates the function Q in the differential equation.
• SOLVE solves a tridiagonal matrix system of the form A*x = b.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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