FEM1D_PACK
1D Finite Element Routines

FEM1D_PACK is a MATLAB library which contains utilities for implementing the finite element method in a 1D region.

Licensing:

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

Languages:

FEM1D_PACK is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

FEM1D, a data directory which contains examples of 1D FEM files, text files that describe a 1D finite element model and associated nodal values.

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

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

FEM1D_FUNCTION_10_DISPLAY, a MATLAB program which reads three files defining a 1D piecewise linear 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_pack_test

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_PROJECT, a MATLAB program which projects data into a finite element space, including the least squares approximation of data, or the projection of a finite element solution from one mesh to another.

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_PACK, a MATLAB library which contains utilities for 2D finite element calculations.

FEM3D_PACK, a MATLAB library which contains utilities for 3D finite element calculations.

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:

• bandwidth_mesh.m computes the bandwidth associated with the finite element mesh;
• legendre_com.m computes abscissas and weights for Gauss-Legendre quadrature.
• local_basis_1d.m evaluates the basis functions in an element.
• local_basis_prime_1d.m evaluates the basis function derivatives in an element.
• local_fem_1d.m evaluates a local finite element function.
• r8_uniform_ab.m returns a pseudorandom R8 in [A,B].
• timestamp.m prints the current YMDHMS date as a time stamp.