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<html>
<head>
<title>
FEM_BASIS_Q4_DISPLAY - Display a Q4 Finite Element Basis Function
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FEM_BASIS_Q4_DISPLAY <br>
Display a Q4 Finite Element Basis Function
</h1>
<hr>
<p>
<b>FEM_BASIS_Q4_DISPLAY</b>
is a MATLAB program which
reads data defining a
bilinear quadrilateral ("Q4") finite element mesh and displays the basis function
associated with any node in the mesh.
</p>
<p>
The entire mesh is shown (which could be a problem for
large meshes!). However, a finite element basis function is
nonzero over only a relatively small number of elements.
Over each one of these elements, the basis function is bilinear, and
it is simple to represent such a shape graphically.
</p>
<p>
The best part of the presentation is that MATLAB allows the
user to turn the plot or zoom in and out, which makes it
much easier to understand the information that is being presented.
</p>
<p>
The quadrilateral mesh is defined by a <i>node file</i> containing
the coordinates of nodes, and an <i>element file</i> containing
sets of the nodes that make up each element.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>fem_basis_q4_display</b> ( <i>'prefix'</i> )
</blockquote>
where
<ul>
<li>
<i>'prefix'</i> is the common file prefix of the files
<i>'prefix'</i><b>_nodes.txt</b> and
<i>'prefix'</i><b>_elements.txt</b>
</li>
</ul>
The user is then queried for node numbers, so that the program
can display the basis function corresponding to that node.
Entering a node number of '0' terminates the program.
</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>FEM_BASIS_Q4_DISPLAY</b> is available in
<a href = "../../m_src/fem_basis_q4_display/fem_basis_q4_display.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Programs:
</h3>
<p>
<a href = "../../m_src/bezier_surface_display/bezier_surface_display.html">
BEZIER_SURFACE_DISPLAY</a>,
a MATLAB program which
displays a Bezier surface.
</p>
<p>
<a href = "../../m_src/fem_50/fem_50.html">
FEM_50</a>,
a MATLAB program which
implements the finite element method in just 50 lines of code.
</p>
<p>
<a href = "../../m_src/fem_50_heat/fem_50_heat.html">
FEM_50_HEAT</a>,
a MATLAB program which
is a modified version of <b>FEM_50</b> suitable
for solving the heat equation.
</p>
<p>
<a href = "../../m_src/fem_basis_t3_display/fem_basis_t3_display.html">
FEM_BASIS_T3_DISPLAY</a>,
a MATLAB program which
displays a basis function associated with a 3-node triangle "T3" mesh.
</p>
<p>
<a href = "../../m_src/fem_basis_t4_display/fem_basis_t4_display.html">
FEM_BASIS_T4_DISPLAY</a>,
a MATLAB program which
displays a basis function associated with a 4-node triangle "T4" mesh.
</p>
<p>
<a href = "../../m_src/fem_basis_t6_display/fem_basis_t6_display.html">
FEM_BASIS_T6_DISPLAY</a>,
a MATLAB program which
displays a basis function associated with a quadratic triangle ("T6") mesh.
</p>
<p>
<a href = "../../m_src/fem_io/fem_io.html">
FEM_IO</a>,
a MATLAB library which
reads and writes the node, element and data files that define a finite element model.
</p>
<p>
<a href = "../../m_src/fem2d_heat/fem2d_heat.html">
FEM2D_HEAT</a>,
a MATLAB program which
solves the time dependent heat equation in the unit square.
</p>
<p>
<a href = "../../m_src/fem2d_pack/fem2d_pack.html">
FEM2D_PACK</a>,
a MATLAB library which
is useful for 2D finite element calculations.
</p>
<p>
<a href = "../../m_src/fem2d_poisson/fem2d_poisson.html">
FEM2D_POISSON</a>,
a MATLAB program which
solves Poisson's equation
on a square, using the finite element method.
</p>
<p>
<a href = "../../m_src/fem2d_sample/fem2d_sample.html">
FEM2D_SAMPLE</a>,
a MATLAB library which
evaluates a finite element function defined on an order 3 or order 6 triangulation.
</p>
<p>
<a href = "../../m_src/polygonal_surface_display/polygonal_surface_display.html">
POLYGONAL_SURFACE_DISPLAY</a>,
a MATLAB program which
reads two files defining a polygonal surface and displays it
within MATLAB.
</p>
<p>
<a href = "../../m_src/quad_surface_display/quad_surface_display.html">
QUAD_SURFACE_DISPLAY</a>,
a MATLAB program which
reads files defining a 3D quadrilateral mesh surface and displays it
within MATLAB.
</p>
<p>
<a href = "../../m_src/tri_surface_display/tri_surface_display.html">
TRI_SURFACE_DISPLAY</a>,
a MATLAB program which
reads data defining a triangular mesh
of a 3D surface and displays it.
</p>
<p>
<a href = "../../c_src/triangle/triangle.html">
TRIANGLE</a>,
a C program which
computes a triangulation of a geometric region.
</p>
<p>
<a href = "../../cpp_src/triangulation_display_opengl/triangulation_display_opengl.html">
TRIANGULATION_DISPLAY_OPENGL</a>,
a C++ program which
reads files defining a triangulation and displays an image
using Open GL.
</p>
<p>
<a href = "../../data/triangulation_order6/triangulation_order6.html">
TRIANGULATION_ORDER6</a>,
a directory which
contains a description and examples of order 6 triangulations.
</p>
<p>
<a href = "../../m_src/triangulation_order6_contour/triangulation_order6_contour.html">
TRIANGULATION_ORDER6_CONTOUR</a>,
a MATLAB program which
can make contours of a scalar quantity defined on the nodes of an order 6
triangulation.
</p>
<p>
<a href = "../../m_src/triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>,
a MATLAB program which
creates an EPS image of a triangulation.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Klaus-Juergen Bathe,<br>
Finite Element Procedures,<br>
Prentice Hall, 1996.
</li>
<li>
Eric Becker, Graham Carey, John Oden,<br>
Finite Elements, An Introduction, Volume I,<br>
Prentice-Hall, 1981.
</li>
<li>
Herbert Edelsbrunner,<br>
Geometry and Topology for Mesh Generation,<br>
Cambridge, 2001,<br>
LC: QA377.E36,<br>
ISBN: 0-521-79309-2.
</li>
<li>
Max Gunzburger,<br>
Finite Element Methods for Viscous Incompressible Flows,<br>
A Guide to Theory, Practice, and Algorithms,<br>
Academic Press, 1989,<br>
LC: TA357.G86.
</li>
<li>
Gilbert Strang, George Fix,<br>
An Analysis of the Finite Element Method,<br>
Prentice Hall, 1973,<br>
LC: TA335.S77.
</li>
</ol>
</p>
<h3 align = "center">
Source code
</h3>
<p>
<ul>
<li>
<a href = "fem_basis_q4_display.m">fem_basis_q4_display.m</a>
gets information about a mesh, and the node for which the
corresponding basis function is desired, and displays a plot.
</li>
</ul>
</p>
<h3 align = "center">
Tests and Examples
</h3>
<p>
<b>HOLE</b>:
<ul>
<li>
<a href = "hole_nodes.txt">hole_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "hole_elements.txt">hole_elements.txt</a>,
the element file.
</li>
<li>
<a href = "hole_node20.png">hole_node20.png</a>,
a PNG image of the basis function at node 20,
</li>
</ul>
</p>
<p>
<b>RECTANGLE</b>:
<ul>
<li>
<a href = "rectangle_nodes.txt">rectangle_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "rectangle_elements.txt">rectangle_elements.txt</a>,
the element file.
</li>
<li>
<a href = "rectangle_node09.png">rectangle_node09.png</a>,
a PNG image of the basis function at node 9.
</li>
</ul>
</p>
<p>
<b>SEMICIRCLE</b>:
<ul>
<li>
<a href = "semicircle_nodes.txt">semicircle_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "semicircle_elements.txt">semicircle_elements.txt</a>,
the element file.
</li>
<li>
<a href = "semicircle_node24.png">semicircle_node24.png</a>,
a PNG image of the basis function at node 24.
</li>
</ul>
</p>
<p>
<b>WEB</b>:
<ul>
<li>
<a href = "web_nodes.txt">web_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "web_elements.txt">web_elements.txt</a>,
the element file.
</li>
<li>
<a href = "web_node83.png">web_node83.png</a>,
a PNG image of the basis function at node 83.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 12 March 2010.
</i>
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