Functions for 1D Finite Elements

**ONED**
is a MATLAB library which
contains functions useful for 1D finite element calculations,
by Jeff Borggaard.

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

**ONED** is available in
a MATLAB version.

FEM1D, a data directory which contains a description of the data files that can be used to describe a 1D finite element model.

FEM_TO_TEC, a MATLAB program which can convert an FEM model into a TEC graphics file.

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

FEM1D_ADAPTIVE, a MATLAB program which applies the finite element method to a linear two point boundary value problem in a 1D region, 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_FUNCTION_10_DISPLAY, a MATLAB program which reads a prefix defining three finite element data files, reads the data, samples the finite element function, and displays a plot.

FEM1D_NONLINEAR, a MATLAB program which applies the finite element method to a nonlinear two point boundary value problem in a 1D region.FEM1D_PACK, a MATLAB library which contains utilities for 1D finite element calculations.

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

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.

HEAT_ONED, a MATLAB program which solves the time-dependent 1D heat equation, using the finite element method in space, and the backward Euler method in time, by Jeff Borggaard.

OPTIMAL_CONTROL_1D, a MATLAB program which seeks the optimal control function for a one dimensional system which is represented using the finite element formulation;

PIECEWISE_LINEAR_PRODUCT_INTEGRAL, a MATLAB library which calculates the exact value of the integral of the product of two piecewise linear functions F(X) and G(X).

THREED, a MATLAB library which contains functions useful for 3D finite element calculations.

TWOD, a MATLAB library which contains functions useful for 2D finite element calculations.

Jeff Borggaard, Virginia Tech.

- oned_bilinear.m integrates kernel(x) * basis function(x) * test function(x).
- oned_f_int.m computes the integral of f(x) times a test function.
- oned_gauss.m sets Gauss integration points on (-1,1).
- oned_gproject.m performs Galerkin projection of a function.
- oned_mesh.m generates a mesh with a prescribed density. This routine returns elements of the same type as xb, e_connb (linear or quadratic)
- oned_plot_hermite.m, plots the Hermite shape functions.
- oned_projectd.m projects the derivative onto the continuous finite element space (this routine simply does a Galerkin projection).
- oned_shape.m computes test functions and derivatives for a Lagrange C0 element given element coordinates and Gauss points. (assumes all nodes are uniformly distributed in the element.)
- oned_shapeherm.m computes test functions and derivatives on a (C1+) Hermite element given element coordinates and Gauss points.
- oned_shapeiso.m computes test functions and derivatives for a isoparametric Lagrange C0 element given element coordinates and Gauss points.

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