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<html>
<head>
<title>
FEM1D - Piecewise Linear Finite Element Method for 1D problem.
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FEM1D <br> Piecewise Linear Finite Element Method for 1D problem.
</h1>
<hr>
<p>
<b>FEM1D</b>
is a C++ program which
applies the finite element method (FEM) to a linear two point
boundary value problem (BVP) in one spatial dimension.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>FEM1D</b> is available in
<a href = "../../c_src/fem1d/fem1d.html">a C version</a> and
<a href = "../../cpp_src/fem1d/fem1d.html">a C++ version</a> and
<a href = "../../f77_src/fem1d/fem1d.html">a FORTRAN77 version</a> and
<a href = "../../f_src/fem1d/fem1d.html">a FORTRAN90 version</a> and
<a href = "../../m_src/fem1d/fem1d.html">a MATLAB version</a> and
<a href = "../../py_src/fem1d/fem1d.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../data/fem1d/fem1d.html">
FEM1D</a>,
a data directory which
contains examples of 1D FEM files,
three text files that describe a 1D finite element model;
</p>
<p>
<a href = "../../cpp_src/fem1d_adaptive/fem1d_adaptive.html">
FEM1D_ADAPTIVE</a>,
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.
</p>
<p>
<a href = "../../cpp_src/fem1d_bvp_linear/fem1d_bvp_linear.html">
FEM1D_BVP_LINEAR</a>,
a C++ program which
applies the finite element method, with piecewise linear elements,
to a two point boundary value problem in one spatial dimension.
</p>
<p>
<a href = "../../cpp_src/fem1d_heat_steady/fem1d_heat_steady.html">
FEM1D_HEAT_STEADY</a>,
a C++ program which
uses the finite element method to solve the steady (time independent)
heat equation in 1D.
</p>
<p>
<a href = "../../cpp_src/fem1d_lagrange/fem1d_lagrange.html">
FEM1D_LAGRANGE</a>,
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.
</p>
<p>
<a href = "../../cpp_src/fem1d_nonlinear/fem1d_nonlinear.html">
FEM1D_NONLINEAR</a>,
a C++ program which
applies the finite
element method to a nonlinear two point boundary value problem
in a 1D region.
</p>
<p>
<a href = "../../cpp_src/fem1d_pack/fem1d_pack.html">
FEM1D_PACK</a>,
a C++ library which
contains utilities for 1D finite element calculations.
</p>
<p>
<a href = "../../cpp_src/fem1d_pmethod/fem1d_pmethod.html">
FEM1D_PMETHOD</a>,
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.
</p>
<p>
<a href = "../../cpp_src/fem1d_project/fem1d_project.html">
FEM1D_PROJECT</a>,
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.
</p>
<p>
<a href = "../../cpp_src/fem1d_sample/fem1d_sample.html">
FEM1D_SAMPLE</a>,
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.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Hans Rudolf Schwarz,<br>
Finite Element Methods,<br>
Academic Press, 1988,<br>
ISBN: 0126330107,<br>
LC: TA347.F5.S3313.
</li>
<li>
Gilbert Strang, George Fix,<br>
An Analysis of the Finite Element Method,<br>
Cambridge, 1973,<br>
ISBN: 096140888X,<br>
LC: TA335.S77.
</li>
<li>
Olgierd Zienkiewicz,<br>
The Finite Element Method,<br>
Sixth Edition,<br>
Butterworth-Heinemann, 2005,<br>
ISBN: 0750663200,<br>
LC: TA640.2.Z54
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "fem1d.cpp">fem1d.cpp</a>, the source code.
</li>
<li>
<a href = "fem1d.sh">fem1d.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "fem1d_output.txt">fem1d_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for FEM1D.
</li>
<li>
<b>ASSEMBLE</b> assembles the matrix and right-hand-side of the linear system.
</li>
<li>
<b>FF</b> evaluates the right hand side function.
</li>
<li>
<b>GEOMETRY</b> sets up the geometry for the interval [XL,XR].
</li>
<li>
<b>INIT</b> assigns values to variables which define the problem.
</li>
<li>
<b>OUTPUT</b> prints out the computed solution.
</li>
<li>
<b>PHI</b> evaluates a linear basis function and its derivative.
</li>
<li>
<b>PP</b> evaluates the function P in the differential equation.
</li>
<li>
<b>PRSYS</b> prints out the tridiagonal linear system.
</li>
<li>
<b>QQ</b> evaluates the function Q in the differential equation.
</li>
<li>
<b>SOLVE</b> solves a tridiagonal matrix system of the form A*x = b.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 31 October 2006.
</i>
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