FEM1D
Three Files Describing a 1D Finite Element Model

FEM1D is a data directory which contains examples of 1D FEM files, which define a 1D finite element model.

The FEM format is a simple dataset of three files that can be used to describe a finite element model.

The finite element model is assumed to include three items:

• Node coordinates (in 1D, 2D or 3D);
• Elements defined by a sequence of node indices (for this simple format, we assume the elements are all of the same order);
• Node values (scalars, vectors, or any set of data);

FEM File Characteristics:

• ASCII
• Each line is one "record"
• Each record is either a comment record or a data record;
• Comment records begin with the "#" character;
• A data record records node coordinates for one node, or the node indices for one element, or the set of node data for one node;
• For a given file, each data record contains the same number of items, separated by blanks.

Licensing:

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

Related Data and Programs:

FEM1D, a C program which applies the finite element method to a 1D linear two point boundary value problem.

FEM1D_ADAPTIVE, a C++ program which applies the finite element method to a 1D linear two point boundary value problem using adaptive refinement to improve the solution.

FEM1D_BVP_LINEAR, a C program which applies the finite element method, with piecewise linear elements, to a two point boundary value problem in one spatial dimension.

FEM1D_NONLINEAR, a C++ program which applies the finite element method to a 1D nonlinear two point boundary value problem.

FEM1D_SAMPLE, a C++ library which evaluates a finite element function defined on an order 3 or order 6 triangulation.

FEM2D, a data directory which contains examples of 2D FEM files, three text files that describe a 2D finite element geometry;

FEM3D, a data directory which contains examples of 3D FEM files, three text files that describe a 3D finite element geometry;

Reference:

1. Hans Rudolf Schwarz,
   Methode der Finiten Elemente,
   Teubner Studienbuecher, 1980,
   ISBN: 3-519-02349-0.
2. Gilbert Strang, George Fix,
   An Analysis of the Finite Element Method,
   Cambridge, 1973,
   ISBN: 096140888X,
   LC: TA335.S77.
3. Olgierd Zienkiewicz,
   The Finite Element Method,
   Sixth Edition,
   Butterworth-Heinemann, 2005,
   ISBN: 0750663200,
   LC: TA640.2.Z54

Sample Files:

ARCTAN is an example of a 1D finite element model, using 29 nodes, and piecewise linear elements, in which a scalar value is stored. The exact solution of the problem is the arctangent function. This data was computed by the FEM1D_ADAPTIVE program.

• arctan_nodes.txt
• arctan_elements.txt
• arctan_values.txt
• arctan.png, a PNG image of the finite element function.

FEM1D is an example of a 1D finite element model, using 11 nodes, and piecewise linear elements, in which a scalar value is stored. This data was computed by the FEM1D_NONLINEAR program.

• fem1d_nodes.txt
• fem1d_elements.txt
• fem1d_values.txt
• fem1d.png, a PNG image of the finite element function.

SIN0 is a degree 0 finite element model for SIN(PI*X) on [0,3].

• sin0_nodes.txt
• sin0_values.txt
• sin0_elements.txt
• sin0.png

SIN1 is a degree 1 finite element model for SIN(PI*X) on [0,3].

• sin1_nodes.txt
• sin1_values.txt
• sin1_elements.txt
• sin1.png

SIN2 is a degree 2 finite element model for SIN(PI*X) on [0,3].

• sin2_nodes.txt
• sin2_values.txt
• sin2_elements.txt
• sin2.png

SIN4 is a degree 4 finite element model for SIN(PI*X) on [0,3].

• sin4_nodes.txt
• sin4_values.txt
• sin4_elements.txt
• sin4.png

SIN8 is a degree 8 finite element model for SIN(PI*X) on [0,3].

• sin8_nodes.txt
• sin8_values.txt
• sin8_elements.txt
• sin8.png

You can go up one level to the DATA directory.