fem1d_project

fem1d_project, a Fortran77 code 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

• sample_prefix_nodes.txt, the node coordinates.
• sample_prefix_values.txt, the data values;

• fem_prefix_nodes.txt, the node coordinates.
• fem_prefix_elements.txt, the nodes that make up each element;
• fem_prefix_values.txt, created by the program, and contains the projections of the data values onto the finite element space, that is, these may be regarded as coefficients of finite element functions representing the projections of the data.

Licensing:

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

Languages:

fem1d_project is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

fem1d_project_test

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

fem1d, a Fortran77 program which applies the finite element method to a 1D linear two point boundary value problem.

FEM1D_ADAPTIVE, a Fortran77 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 Fortran77 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 Fortran77 program which applies the finite element method to a 1D nonlinear two point boundary value problem.

FEM1D_PMETHOD, a Fortran77 program which applies the p-method version of the finite element method to a 1D linear two point boundary value problem.

FEM1D_SAMPLE, a Fortran77 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 Fortran90 program which projects a function F(X,Y) into a given finite element space of piecewise linear triangular 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:

• fem1d_project.f, the source code.
• fem1d_project.sh, commands to compile the source code.