FEM1D_PROJECT
Project Data onto a 1D Finite Element Mesh


FEM1D_PROJECT is a MATLAB program which computes the projection of sample data onto a given finite element mesh.

This procedure can be used to determine the least squares approximant to data (actually, to the piecewise linear interpolant of that data) or to determine the finite element coefficients appropriate when recomputing a finite element solution from a fine mesh to a coarse mesh.

The sample data is given simply as two files, one containing the points, the other, the corresponding data values.

The user must also supply two files defining the finite element mesh, containing the points, and the pairs of points that form the elements.

The program takes the sample data, projects it onto the finite element mesh, and determines a file of finite element coefficients that represent the projection of the data onto the finite element space.

The current version of the program can only handle finite element meshes which are made of piecewise linear basis functions.

Usage:

fem1d_project ( 'sample_prefix', 'fem_prefix' )
where 'sample_prefix' is the common prefix for the SAMPLE files: and 'fem_prefix' is the common prefix for the FEM files:

Licensing:

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

Languages:

FEM1D_PROJECT is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

FEM1D, a data directory which contains examples of 1D FEM files, three text files that describe a 1D finite element model;

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

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

FEM1D_DISPLAY, a MATLAB program which reads three files defining a 1D arbitrary degree finite element function, and displays a plot.

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

FEM1D_PMETHOD, a MATLAB program which applies the p-method version of the finite element method to a 1D linear two point boundary value problem.

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

FEM2D_PROJECT_FUNCTION, a MATLAB program which projects a function F(X,Y), given as a formula, into a given finite element space of piecewise linear triangular elements.

FEM3D_PROJECT, a MATLAB program which projects a function F(X,Y,Z), given as a data, into a given finite element space of piecewise linear tetrahedral elements.

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:

Examples and Tests:

POWERS starts with sample data for the vector function f(x)=[ 1, x, x^2], on a grid of 11 equally spaced nodes from 0 to 10, and projects this onto a piecewise linear grid of 6 equally spaced nodes from 0 to 10.

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


Last revised on 05 August 2009.