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<html>
<head>
<title>
FEM2D_BVP_SERENE - Finite Element Method, 2D, Boundary Value Problem, Serendipity Elements
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FEM2D_BVP_SERENE <br> Finite Element Method, 2D, Boundary Value Problem, Serendipity Elements
</h1>
<hr>
<p>
<b>FEM2D_BVP_SERENE</b>
is a C++ program which
applies the finite element method, with serendipity elements,
to a 2D boundary value problem over a rectangle.
</p>
<p>
The boundary value problem (BVP) that is to be solved has the form:
<pre>
- d/dx ( a(x,y) * du/dx ) - d/dy ( a(x,y) * du/dy ) + c(x,y) * u(x,y) = f(x,y)
</pre>
This equation holds in the interior of some rectangle R.
The functions a(x,y), c(x,y), and f(x,y) are given.
</p>
<p>
Zero boundary conditions are imposed on the boundary of R.
</p>
<p>
The MATLAB "gallery()" command can produce a copy of the Wathen matrix,
which arises as a weighted sum of elementary mass matrices associated
with a grid of serendipity elements.
</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>
<h3 align = "center">
Languages:
</h3>
<p>
<b>FEM2D_BVP_SERENE</b> is available in
<a href = "../../c_src/fem2d_bvp_serene/fem2d_bvp_serene.html">a C version</a> and
<a href = "../../cpp_src/fem2d_bvp_serene/fem2d_bvp_serene.html">a C++ version</a> and
<a href = "../../f77_src/fem2d_bvp_serene/fem2d_bvp_serene.html">a FORTRAN77 version</a> and
<a href = "../../f_src/fem2d_bvp_serene/fem2d_bvp_serene.html">a FORTRAN90 version</a> and
<a href = "../../m_src/fem2d_bvp_serene/fem2d_bvp_serene.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/fem2d_bvp_linear/fem2d_bvp_linear.html">
FEM2D_BVP_LINEAR</a>,
a C++ program which
applies the finite element method (FEM), with piecewise linear
elements, to a 2D boundary value problem (BVP) over a rectangle,
and compares the computed and exact solutions
with the L2 and seminorm errors.
</p>
<p>
<a href = "../../cpp_src/fem2d_bvp_quadratic/fem2d_bvp_quadratic.html">
FEM2D_BVP_QUADRATIC</a>,
a C++ program which
applies the finite element method (FEM), with piecewise quadratic
elements, to a 2D boundary value problem (BVP) over a rectangle,
and compares the computed and exact solutions
with the L2 and seminorm errors.
</p>
<p>
<a href = "../../cpp_src/wathen/wathen.html">
WATHEN</a>,
a C++ library which
compares storage schemes (full, banded, sparse triplet, sparse) and
solution strategies (A\x, Linpack, conjugate gradient (CG))
for linear systems involving the Wathen matrix,
which can arise when solving a problem using the
finite element method (FEM).
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "fem2d_bvp_serene.cpp">fem2d_bvp_serene.cpp</a>, the source code.
</li>
<li>
<a href = "fem2d_bvp_serene.hpp">fem2d_bvp_serene.hpp</a>, the include file.
</li>
<li>
<a href = "fem2d_bvp_serene.sh">fem2d_bvp_serene.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "fem2d_bvp_serene_prb.cpp">fem2d_bvp_serene_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "fem2d_bvp_serene_prb.sh">fem2d_bvp_serene_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "fem2d_bvp_serene_prb_output.txt">fem2d_bvp_serene_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BASIS_SERENE</b> evaluates the serendipity basis functions.
</li>
<li>
<b>BASIS_DX_SERENE</b> differentiates the serendipity basis functions.
</li>
<li>
<b>BASIS_DY_SERENE</b> differentiates the serendipity basis functions.
</li>
<li>
<b>FEM2D_BVP_SERENE</b> solves boundary value problem on a rectangle.
</li>
<li>
<b>FEM2D_BVP_SERENE_NODE_NUM</b> counts the number of nodes.
</li>
<li>
<b>FEM2D_H1S_ERROR_SERENE:</b> seminorm error of a finite element solution.
</li>
<li>
<b>FEM2D_L1_ERROR_SERENE:</b> l1 error norm of a finite element solution.
</li>
<li>
<b>FEM2D_L2_ERROR_SERENE:</b> L2 error norm of a finite element solution.
</li>
<li>
<b>NOT1</b> evaluates a factor for serendipity basis functions.
</li>
<li>
<b>NOT1D</b> differentiates a factor for serendipity basis functions.
</li>
<li>
<b>NOT2</b> evaluates a factor for serendipity basis functions.
</li>
<li>
<b>NOT2DX</b> evaluates a factor for serendipity basis functions.
</li>
<li>
<b>NOT2DY</b> evaluates a factor for serendipity basis functions.
</li>
<li>
<b>R8MAT_PRINT</b> prints an R8MAT.
</li>
<li>
<b>R8MAT_PRINT_SOME</b> prints some of an R8MAT.
</li>
<li>
<b>R8MAT_SOLVE2</b> computes the solution of an N by N linear system.
</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 07 July 2014.
</i>
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