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      FEM1D - Piecewise Linear Finite Element Method for 1D problem.
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      FEM1D <br> Piecewise Linear Finite Element Method for 1D problem.
    </h1>

    <hr>

    <p>
      <b>FEM1D</b> 
      is a FORTRAN77 program which 
      applies the finite element method to a linear two point
      boundary value problem in one spatial dimension.
    </p>

    <h3 align = "center">
      Licensing:
    </h3>

    <p>
      The computer code and data files described and made available on this web page 
      are distributed under
      <a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
    </p>

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      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>
    </p>

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      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 = "../../f77_src/fem1d_adaptive/fem1d_adaptive.html">
      FEM1D_ADAPTIVE</a>,
      a FORTRAN77 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 = "../../f77_src/fem1d_bvp_linear/fem1d_bvp_linear.html">
      FEM1D_BVP_LINEAR</a>,
      a FORTRAN77 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 = "../../f77_src/fem1d_nonlinear/fem1d_nonlinear.html">
      FEM1D_NONLINEAR</a>, 
      a FORTRAN77 program which
      applies the finite
      element method to a nonlinear two point boundary value problem
      in a 1D region.
    </p>

    <p>
      <a href = "../../f77_src/fem1d_pmethod/fem1d_pmethod.html">
      FEM1D_PMETHOD</a>, 
      a FORTRAN77 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 = "../../f77_src/fem1d_project/fem1d_project.html">
      FEM1D_PROJECT</a>, 
      a FORTRAN77 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 = "../../f77_src/fem1d_sample/fem1d_sample.html">
      FEM1D_SAMPLE</a>,
      a FORTRAN77 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>

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      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>

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      Source Code:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "fem1d.f">fem1d.f</a>, the source code.
        </li>
        <li>
          <a href = "fem1d.sh">fem1d.sh</a>,
          commands to compile the source code.
        </li>
      </ul>
    </p>

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      Examples and tests:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "fem1d_output.txt">fem1d_output.txt</a>, 
          the output file.
        </li>
      </ul>
    </p>

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      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>MAIN</b> is the main program for FEM1D.
        </li>
        <li>
          <b>ASSEMB</b> assembles the matrix and the right-hand-side.
        </li>
        <li>
          <b>FF</b> evaluates the function F in the differential equation.
        </li>
        <li>
          <b>GEOMET</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>
      </ul>
    </p>

    <p>
      You can go up one level to <a href = "../f77_src.html">
      the FORTRAN77 source codes</a>.
    </p>

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    <i>
      Last revised on 31 October 2006.
    </i>

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