FEM_BASIS_T4_DISPLAY
Display a T4 Finite Element Basis Function

FEM_BASIS_T4_DISPLAY is a MATLAB program which reads data defining a T4 mesh of 4-node triangles, and displays the basis function associated with any node in the mesh.

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 these elements, the basis function is cubic, and the curved nature of this part of the surface is suggested by taking many plot points in this region.

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.

The triangular mesh is defined by a node file containing the coordinates of nodes, and an element file containing sets of the four nodes that make up each element.

Note that the four nodes making up each element are to be listed in a particular order, in which the vertices come first, followed by the centroid, as suggested by the following diagram:

        3
        |\
        | \
        |  \
        |   \
        | 4  \
        |     \
        |      \
        1-------2
      

Usage:

fem_basis_t4_display ( 'prefix' )

• 'prefix' is the common filename prefix of the node file 'prefix'_nodes.txt and the element file 'prefix'_elements.txt

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Programs:

BEZIER_SURFACE_DISPLAY, a MATLAB program which displays a Bezier surface.

FEM_50, a MATLAB program which implements a finite element method in just 50 lines of code.

FEM_50_HEAT, a MATLAB program which is a modified version of FEM_50 suitable for solving the heat equation.

FEM_BASIS_T3_DISPLAY, a MATLAB program which displays a basis function associated with a 3-node T3 mesh.

FEM_BASIS_T6_DISPLAY, a MATLAB program which displays a basis function associated with a 6-node T6 mesh.

FEM_IO, a MATLAB library which reads and writes the node, element and data files that define a finite element model.

FEM2D_HEAT, a MATLAB program which solves the time dependent heat equation in the unit square.

FEM2D_PACK, a MATLAB library which is useful for 2D finite element calculations.

FEM2D_POISSON, a MATLAB program which solves Poisson's equation on a square, using the finite element method.

FEM2D_SAMPLE, a MATLAB library which evaluates a finite element function defined on an order 3 or order 6 triangulation.

POLYGONAL_SURFACE_DISPLAY, a MATLAB program which reads two files defining a polygonal surface and displays it within MATLAB.

QUAD_SURFACE_DISPLAY, a MATLAB program which reads files defining a 3D quadrilateral mesh surface and displays it within MATLAB.

TET_MESH_DISPLAY, a MATLAB program which can read in the node and tetra files defining a tet mesh and display a wireframe image.

TRI_SURFACE_DISPLAY, a MATLAB program which reads data defining a triangular mesh of a 3D surface and displays it.

TRIANGLE, a C program which computes a triangulation of a geometric region.

TRIANGULATION_DISPLAY_OPENGL, a C++ program which reads files defining a triangulation and displays an image using Open GL.

TRIANGULATION_ORDER6, a directory which contains a description and examples of order 6 triangulations.

TRIANGULATION_ORDER6_CONTOUR, a MATLAB program which can make contours of a scalar quantity defined on the nodes of an order 6 triangulation.

TRIANGULATION_PLOT, a MATLAB program which creates an EPS image of a triangulation.

Reference:

1. Klaus-Juergen Bathe,
   Finite Element Procedures,
   Prentice Hall, 1996.
2. Eric Becker, Graham Carey, John Oden,
   Finite Elements, An Introduction, Volume I,
   Prentice-Hall, 1981.
3. Herbert Edelsbrunner,
   Geometry and Topology for Mesh Generation,
   Cambridge, 2001,
   LC: QA377.E36,
   ISBN: 0-521-79309-2.
4. Max Gunzburger,
   Finite Element Methods for Viscous Incompressible Flows,
   A Guide to Theory, Practice, and Algorithms,
   Academic Press, 1989,
   LC: TA357.G86.
5. Gilbert Strang, George Fix,
   An Analysis of the Finite Element Method,
   Prentice Hall, 1973,
   LC: TA335.S77.

Source code:

• fem_basis_t4_display.m the source code.

Tests and Examples

RECTANGLE is a simple 5 by 4 mesh of 44 nodes and 24 elements. Files you may copy include:

• rectangle_nodes.txt, the node file.
• rectangle_nodes.png, a PNG image of the nodes.
• rectangle_elements.txt, the element file.
• rectangle_elements.png, a PNG image of the elements.
• basis12.png, a PNG image of the basis function associated with node 12.
• basis35.png, a PNG image of the basis function associated with node 35.

You can go up one level to the MATLAB source codes.