fem1d_lagrange/fem1d_lagrange.html

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      FEM1D_LAGRANGE - 1D Finite Element Code Using Lagrange Basis Polynomials
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      FEM1D_LAGRANGE <br> 1D Finite Element Code Using Lagrange Basis Polynomials
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    <p>
      <b>FEM1D_LAGRANGE</b>
      is a MATLAB 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>

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      Licensing:
    </h3>

    <p>
      The computer code and data files 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_LAGRANGE</b> is available in
      <a href = "../../c_src/r8lib/r8lib.html">a C version</a> and
      <a href = "../../cpp_src/r8lib/r8lib.html">a C++ version</a> and
      <a href = "../../f77_src/r8lib/r8lib.html">a FORTRAN77 version</a> and
      <a href = "../../f_src/r8lib/r8lib.html">a FORTRAN90 version</a> and
      <a href = "../../m_src/r8lib/r8lib.html">a MATLAB version</a>.
    </p>

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      Related Programs:
    </h3>

    <p>
      <a href = "../../m_src/fem1d/fem1d.html">
      FEM1D</a>,
      a MATLAB program which
      applies the finite element method (FEM) to a 1D linear two point
      boundary value problem (BVP).
    </p>

    <p>
      <a href = "../../m_src/fem1d_spectral_numeric/fem1d_spectral_numeric.html">
      FEM1D_SPECTRAL_NUMERIC</a>,
      a MATLAB program which
      applies the spectral finite element method (FEM) to solve the 
      two point boundary value problem (BVP_
      u'' = - pi^2 sin(x) over [-1,+1] with zero boundary conditions,
      using as basis elements the functions x^n*(x-1)*(x+1),
      and carrying out the integration numerically, 
      using MATLAB's quad() function,
      by Miro Stoyanov.
    </p>

    <p>
      <a href = "../../m_src/lagrange_interp_1d/lagrange_interp_1d.html">
      LAGRANGE_INTERP_1D</a>,
      a MATLAB library which
      defines and evaluates the Lagrange polynomial p(x) 
      which interpolates a set of data, so that p(x(i)) = y(i).
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      Source Code:
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    <p>
      <ul>
        <li>
          <a href = "fem1d_lagrange_stiffness.m">fem1d_lagrange_stiffness.m</a>
          computes the stiffness matrix, mass matrix, and right hand side
          for a finite element problem that uses Lagrange basis polynomials.
        </li>
        <li>
          <a href = "lagrange_derivative.m">lagrange_derivative.m</a>,
          evaluates the derivative of Lagrange basis polynomials.
        </li>
        <li>
          <a href = "lagrange_value.m">lagrange_value.m</a>,
          evaluates the Lagrange basis polynomials.
        </li>
        <li>
          <a href = "legendre_set.m">legendre_set.m</a>,
          sets the points and weights of a Legendre quadrature rule.
        </li>
        <li>
          <a href = "r8vec_print.m">r8vec_print.m</a>,
          prints an R8VEC.
        </li>
        <li>
          <a href = "timestamp.m">timestamp.m</a>,
          prints the current YMDHMS date as a timestamp;
        </li>
      </ul>
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      Examples and Tests:
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      <ul>
        <li>
          <a href = "fem1d_lagrange_test.m">fem1d_lagrange_test.m</a>,
          runs all the tests;
        </li>
        <li>
          <a href = "fem1d_lagrange_test_output.txt">fem1d_lagrange_test_output.txt</a>,
          the output file;
        </li>
        <li>
          <a href = "fem1d_lagrange_stiffness_test.m">fem1d_lagrange_stiffness_test.m</a>
        </li>
        <li>
          <a href = "lagrange_derivative_test.m">lagrange_derivative_test.m</a>
        </li>
        <li>
          <a href = "lagrange_value_test.m">lagrange_value_test.m</a>
        </li>
        <li>
          <a href = "legendre_set_test.m">legendre_set_test.m</a>
        </li>
      </ul>
    </p>

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

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    <i>
      Last revised on 16 November 2014.
    </i>

    <!-- John Burkardt -->

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