FEM2D_SAMPLE
Evaluate a Finite Element Function of a 2D Argument

FEM2D_SAMPLE is a MATLAB program which evaluates a finite element function of a 2D argument.

The current version of the program can only handle finite element meshes which are made of piecewise linear triangles of order 3 or 6.

Usage:

fem2d_sample ( 'fem_prefix', 'sample_prefix' )

• 'fem_prefix'_nodes.txt, the node coordinates.
• 'fem_prefix'_elements.txt, the nodes that make up each element;
• 'fem_prefix'_values.txt, the values defined at each node.

• 'sample_prefix'_nodes.txt, the node coordinates where samples are desired.
• 'sample_prefix'_values.txt, the values computed at each sample node.

Licensing:

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

Languages:

FEM2D_SAMPLE is available in a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

DISCRETE_PDF_SAMPLE, a MATLAB program which demonstrates how to construct a Probability Density Function (PDF) from a table of sample data, and then to use that PDF to create new samples.

FEM1D_SAMPLE, a MATLAB program which samples a scalar or vector finite element function of one variable, defined by FEM files, returning interpolated values at the sample points.

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

FEM2D_HEAT, a MATLAB program which solves the 2D time dependent heat equation on the unit square.

FEM2D_NAVIER_STOKES, a MATLAB program which solves the 2D incompressible Navier Stokes equations in an arbitrary triangulated region.

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

FEM2D_POISSON, a MATLAB program which solves the 2D Poisson equation on a square, using the finite element method.

FEM2D_PROJECT, a MATLAB program which projects a function F(X,Y) into a given finite element space of piecewise linear triangular elements.

FEM2D_STOKES, a MATLAB program which solves the 2D incompressible Stokes equations in an arbitrary triangulated region.

FEM3D_SAMPLE, a MATLAB program which evaluates a finite element function defined on 3D tetrahedral mesh.

Reference:

1. Hans Rudolf Schwarz,
   Finite Element Methods,
   Academic Press, 1988,
   ISBN: 0126330107,
   LC: TA347.F5.S3313..
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.

Source Code:

• fem2d_sample.m is the source code.

Examples and Tests:

SQ is FEM data for the function f(x,y)=x^2+y^2, on a 5x5 grid of nodes, organized into linear triangles. The sample data seeks the values of this function on a 4x4 evenly spaced grid.

• fem_sq_nodes.txt, defines the FEM nodes.
• fem_sq_elements.txt, defines the FEM elements.
• fem_sq_values.txt, defines the FEM nodal values.
• sample_sq_nodes.txt, defines the sample nodes.
• sample_sq_values.txt, defines the sample nodal values.

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